IT LITERALLY SAYS 0.9999999... HOW CAN IT BE 1? Prove it robustly without a bunch of algebra handwaving

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Anonymous Mon Jan 9 16:55:21 2023 No.15111209 [Reply] [Original]

IT LITERALLY SAYS 0.9999999... HOW CAN IT BE 1? Prove it robustly without a bunch of algebra handwaving

>>	Anonymous Mon Jan 9 16:57:07 2023 No.15111211 >>15111209 What is the definition of this thing as a real number?

>>	Anonymous Mon Jan 9 16:59:50 2023 No.15111216 >>15111209 So? It doesn't have to look like 1.000 to be equal to 1.000

>>	Anonymous Mon Jan 9 17:05:00 2023 No.15111226 >>15111209 2/2 also literally says 2/2. It's still 1 though.

>>	Anonymous Mon Jan 9 17:07:58 2023 No.15111230 >>15111209 wikipedia is a good starting point

>>	Anonymous Mon Jan 9 17:11:44 2023 No.15111235 >>15111209 >IT LITERALLY SAYS 1+1 HOW CAN IT BE 2?

>>	Anonymous Mon Jan 9 17:15:50 2023 No.15111238 >>15111211 >>15111216 >>15111226 >>15111230 >>15111235 >No robust arguments

>>	Anonymous Mon Jan 9 17:18:06 2023 No.15111243 >>15111238 >can't be bothered by reading any of the proof that's already there. . .

>>	Anonymous Mon Jan 9 17:19:29 2023 No.15111246 >>15111243 its not proof its algebra handwaving and bogus walmart logic

>>	Anonymous Mon Jan 9 17:19:58 2023 No.15111249 >>15111209 It follows from the assumption that if some number x satisfies x ≤ 1/n for all natural numbers n, then x ≤ 0. >how do you know that? You don't. It's an assumption.

>>	Anonymous Mon Jan 9 17:21:27 2023 No.15111254 File: 8 KB, 205x246, 1664875776204329.jpg [View same] [iqdb] [saucenao] [google] >>15111209 >So? It doesn't have to look like 1.000 to be equal to 1.000

>>	Anonymous Mon Jan 9 17:34:08 2023 No.15111276 >>15111209 could you give me a real number between 0.999... and 1 ? here is your proof

>>	Anonymous Mon Jan 9 17:34:32 2023 No.15111277 >>15111249 okay i'll just assume that 0.99999... =/= 1 instead then

>>	Anonymous Mon Jan 9 17:35:56 2023 No.15111279 >>15111276 0.9999... and put and another nine at the end of it

>>	Anonymous Mon Jan 9 17:37:04 2023 No.15111283 >>15111277 Then you have to accept that there are numbers that are larger than 0 but smaller than every 1/n.

>>	Anonymous Mon Jan 9 17:38:28 2023 No.15111285 >>15111283 yes ill just assume that

>>	Anonymous Mon Jan 9 17:40:31 2023 No.15111290 >>15111279 this is supposed to be an infinite sequence yet I admit its abusive notation

>>	Anonymous Mon Jan 9 17:40:41 2023 No.15111291 >>15111285 good

>>	Anonymous Mon Jan 9 17:50:55 2023 No.15111315 1/3 = 0.333333333…. right? And 0.3333333… + 0.333333… + 0.33333… equals 0.9999999…. But 1/3 + 1/3 + 1/3 equals….

>>	Anonymous Mon Jan 9 17:52:42 2023 No.15111321 >>15111315 >1/3 = 0.333333333…. right? Prove it.

>>	Anonymous Mon Jan 9 17:52:46 2023 No.15111322 >>15111315 0.33333... is irrational >why? By assumption

>>	Anonymous Mon Jan 9 17:56:14 2023 No.15111330 >>15111209 >HOW CAN IT BE 9/inf=0

>>	Anonymous Mon Jan 9 17:58:43 2023 No.15111341 >>15111315 >1/3 = 0.333333333…. right? no

>>	Anonymous Mon Jan 9 17:59:05 2023 No.15111342 >>15111321 1/3 = 3/10 + 1/30 = 0.3 + 1/30 = 0.33 + 1/300 = 0.333 + 1/3000 : = 0.3... + 1/inf = 0.3... + 0 = 0.3...

Anonymous Mon Jan 9 18:03:14 2023 No.15111350

>>15111342
infinities not a number, you can't divide by it.
you can only take the limit of that fraction as the denominator approaches an arbitrarily large number. But, the limit is never the same as the actual value.
There exists no number such that n times 0 = 1
so there would be no number you divide 1 by to get 0.

>>	Anonymous Mon Jan 9 18:06:23 2023 No.15111357 >>15111209 for every rational number less than 1, 0.999… is strictly greater than it. and since 0.999… is obviously not greater than 1, and since the rational numbers are dense, we can conclude that 0.999… must be equal to 1. questions?

Anonymous Mon Jan 9 18:08:35 2023 No.15111358

>>15111350
>infinities not a number, you can't divide by it.
sure you can, and more:
1/inf = 0
0/inf = 0
1 + inf = inf
1 - inf = -inf
inf + inf = inf
inf/inf undefined
inf - inf undefined
1^inf undefined

you can't do everything with inf as with a number, doesn't mean you can do nothing tho

>>	Anonymous Mon Jan 9 18:13:31 2023 No.15111372 >>15111342 >= 0.333 + 1/3000 >... >= 0.3... + 1/inf I like how you conveninetly marked the nonsequitur as with those dots.

>>	Anonymous Mon Jan 9 18:15:40 2023 No.15111374 >>15111358 it isn't even a number, its a concept. all that stuff you wrote is just wrong.

>>	Anonymous Mon Jan 9 18:16:59 2023 No.15111379 The reals are dense; between any two non-equal reals are more reals. Therefore, if 2 reals DO NOT have any reals between them, they must be equal.

>>	Anonymous Mon Jan 9 18:18:04 2023 No.15111380 >>15111374 You're a big gay and you should have let me handle it instead of jumping in. His mistake is a lot more basic and a lot less up for debate than what you think it is.

>>	Anonymous Mon Jan 9 18:20:06 2023 No.15111383 >>15111379 so any two consecutive reals are equal? using this logic, any real consecutive to a real consecutive to another real would also be equal. Then, this continuing endless would mean all reals are equal to each other.

>>	Anonymous Mon Jan 9 18:22:35 2023 No.15111388 >>15111383 no two reals can be “consecutive” since theres always one in between.

>>	Anonymous Mon Jan 9 18:22:36 2023 No.15111389 >>15111209 >HOW CAN IT BE 1? its a trivial proof left as an exercise to the reader

Anonymous Mon Jan 9 18:27:47 2023 No.15111402

>>15111209
Proof by Dedekind cut:

Assume to contradiction that x is a rational number such that

0.999... < x < 1

0.999... is greater than any finite string of 9s so for any natural number n

1-1/10^n < 0.999... < x < 1

1-x < 1/10^n

10^n < 1/(1-x)

n < log(1/(1-x))

Let n = ceiling(log(1/(1-x)))+1

ceiling(log(1/(1-x)))+1 < log(1/(1-x))

This is a contradiction, so x does not exist and 0.999... = 1.

>>	Anonymous Mon Jan 9 18:36:11 2023 No.15111415 File: 178 KB, 779x778, 1648642699510.jpg [View same] [iqdb] [saucenao] [google] >>15111380 i don't want to be a big gay

>>	Anonymous Mon Jan 9 18:38:45 2023 No.15111421 >>15111380 bro wtf apologize

>>	Anonymous Mon Jan 9 18:38:48 2023 No.15111422 >>15111402 now prove it using cauchy sequences

>>	Anonymous Mon Jan 9 18:39:43 2023 No.15111423 >>15111422 Via Cauchy sequences: 0.999... = (0.9, 0.99, 0.999,...) = lim as n-> inf of 1-1/10^n = 1

>>	Anonymous Mon Jan 9 18:41:21 2023 No.15111426 The difference is infinitesimal. If you have an object that measures 0.999 cm and your ruler has a 0.001 cm precision on the measurement, you won't be able to tell 0.999 and 1.000 apart. This is the same but at the mathematical level.

>>	Anonymous Mon Jan 9 18:41:29 2023 No.15111427 >>15111209 0.9999... = x 9.9999... = 10x 9 = 9x x = 1 1 = x = 0.9999...

>>	Anonymous Mon Jan 9 18:42:28 2023 No.15111431 >>15111426 Excruciatingly retarded post.

>>	Anonymous Mon Jan 9 18:45:45 2023 No.15111436 >>15111427 You're being dishonest. 0.9999 = x 9.9990 = 10x 9.9990 - 0.9999 = 9x 8.9991 = 9x x = 8.9991/9 x = 0.9999 This is true for any number of 9s.

>>	Anonymous Mon Jan 9 18:47:57 2023 No.15111438 >>15111427 how did you get from the second line to the third

>>	Anonymous Mon Jan 9 18:49:45 2023 No.15111442 File: 47 KB, 645x729, 8d6.jpg [View same] [iqdb] [saucenao] [google] >>15111436 >you're being dishonest because your argument is correct

>>	Anonymous Mon Jan 9 18:50:47 2023 No.15111444 >>15111438 Subtract x=0.999... from both sides.

>>	Anonymous Mon Jan 9 18:54:47 2023 No.15111450 >>15111444 you'd get 9.00....1x on the right then

>>	Anonymous Mon Jan 9 18:56:08 2023 No.15111454 >>15111450 No, 10x-x = 9x. Need to go back to kindergarten?

>>	Anonymous Mon Jan 9 18:57:27 2023 No.15111461 >>15111454 you took away .9999... not 1. you can't assume they are equal and use it to prove they are equal

>>	Anonymous Mon Jan 9 18:57:33 2023 No.15111462 >>15111442 In mathematical notation, because 0.999... is not rigorous. [math] 0.999... = \lim \sum_{k=1}^{n}\frac{9}{10^k} [/math]

>>	Anonymous Mon Jan 9 18:59:38 2023 No.15111465 >>15111461 >you took away .9999... not 1 Not me, but yes, that's what he did. 9.999... - 0.999... = 9. 10x -x = 9x >you can't assume they are equal Where was this assumed? x was subtracted, not 1. Need to go back to kindergarten?

>>	Anonymous Mon Jan 9 19:00:56 2023 No.15111469 >>15111462 It's rigorous, and your objection that his argument results in true statements like 0.9999 = 0.9999 is nonsensical.

>>	Anonymous Mon Jan 9 19:03:11 2023 No.15111475 >>15111374 W-A agrees with >>15111358

>>	Anonymous Mon Jan 9 19:03:55 2023 No.15111477 >>15111469 He's making a valid point and you're the retard. 0.9999... = x is a nonsensical statement until you define what the infinite sum it alludes to sums up to, which is what you have to prove in the first place.

Anonymous Mon Jan 9 19:09:01 2023 No.15111491

>>15111477
>He's making a valid point and you're the retard. 0.9999... = x is a nonsensical statement until you define what the infinite sum it alludes to sums up to
No, that's not how math works. That's as silly as saying you need to define the exact value of x before solving x^2-2x+1 = 0. And that has nothing to do with his initial objection, which is proof enough that he's retarded, since he thinks the same argument making correct conclusions about finite strings of 9s invalidates it.

>>	Anonymous Mon Jan 9 19:11:14 2023 No.15111501 >>15111477 It's not a sum, it's a Fedekind cut or Cauchy sequence. Retard.

>>	Anonymous Mon Jan 9 19:11:35 2023 No.15111505 >>15111465 sorry, you are right. but the real problem with his proof is that he put .999... x 10 = 9.999... which isn't true.

>>	Anonymous Mon Jan 9 19:13:19 2023 No.15111508 >>15111505 It is by definition of base 10. Multiplication by the base moves the decimal one place to the right.

>>	Anonymous Mon Jan 9 19:14:43 2023 No.15111510 >>15111374 >all that stuff you wrote is just wrong. prove it

Anonymous Mon Jan 9 19:14:44 2023 No.15111511

>>15111491
That's as silly as saying you need to define the exact value of x before solving x^2-2x+1 = 0.
No, you imbecile. If anything, it's like saying you need to define what the values of the symbo;s '1' and '0' are.

>>15111501
Take your actual meds.

>>	Anonymous Mon Jan 9 19:14:51 2023 No.15111512 >>15111462 .999... doesn't equal the limit of that sum.

>>	Anonymous Mon Jan 9 19:16:32 2023 No.15111515 >>15111512 >source: my ass

>>	Anonymous Mon Jan 9 19:17:16 2023 No.15111519 >>15111508 yes. thanks to base 10 we know that if a number is multiplied by then, and moves one place to the right, the now empty space is a 0, not a 9. .999... x10 = .999...90

>>	Anonymous Mon Jan 9 19:17:23 2023 No.15111520 >>15111511 >If anything, it's like saying you need to define what the values of the symbo;s '1' and '0' are. Yes, which is equally retarded, since we already know what they mean. >Take your actual meds. LOL, you lost.

>>	Anonymous Mon Jan 9 19:18:03 2023 No.15111521 >>15111520 >we already know what they mean Literal subhuman level of intellect.

>>	Anonymous Mon Jan 9 19:18:18 2023 No.15111523 >>15111515 >you need a source for a definition

>>	Anonymous Mon Jan 9 19:18:46 2023 No.15111525 >>15111519 >the now empty space is a 0 What empty space? Moving the decimal doesn't create new digits, it simply shifts them. There is no 0, only 9s.

>>	Anonymous Mon Jan 9 19:19:53 2023 No.15111526 >>15111521 I agree, if you don't know what 0 and 1 refer to then you have literal subhuman level of intellect.

>>	Anonymous Mon Jan 9 19:22:50 2023 No.15111533 >>15111526 They don't refer to anything until they're defined, subhuman. Thanks for going out of your way to demonstrate your mental deficiency.

>>	Anonymous Mon Jan 9 19:24:40 2023 No.15111538 >>15111533 They are defined, you would already know the definitions if you weren't a subhuman.

>>	Anonymous Mon Jan 9 19:29:02 2023 No.15111552 >>15111538 >They are defined I didn't say they weren't. Every time you post, you demonstrate the necessity of eugenics. The worthless animal you call your mother should have been sterilized.

Anonymous Mon Jan 9 19:33:16 2023 No.15111566

>>15111525
.999... is a placeholder for a decimal expansion with an arbitrarily large natural number of digits.
all natural numbers are finite. so no matter what arbitrarily large natural number is chosen, it will be finite. so, once the decimal expansion has reached this arbitrarily large number of digits, it would stop. there would be no more 9s to the right. multiplying it by 10 would then change the digit in the place of place in the decimal expansion of the final 9 to a 0, reducing the number of 9s to the right of the decimal point by 1, and increasing the number to the left of it by 1. therefore, its not the same number as .999... + 9, since that would have 1 more 9 digit than .999... x10 would.
all natural numbers are finite. that is the core of the argument.

Anonymous Mon Jan 9 19:39:20 2023 No.15111583

>>15111436
Just because something is true for any number of numbers doesn't mean it is true with an infinitie number of numbers.
Imagine you have an infinite number of balls with a natural number written on it which you put into a box. The rules are that you put balls into the box in order of their label, and when you get a number which is a perfect square (eg 4), you take out the number which is its square root (eg 2). For an infinite number of turns, the box will be empty as every number has a square. However, for any number of turns, the box will be nonzero since evry turn either adds a ball (when it is not a perfect square) or keeps the same number of balls (exchanges a square root for its perfect square)

>>	Anonymous Mon Jan 9 19:41:00 2023 No.15111589 1/9 = 0.111... + 8/9 = 0.888... = 9/9 = 0.999...

>>	Anonymous Mon Jan 9 19:42:23 2023 No.15111593 >>15111552 >I didn't say they weren't Then your objection "They don't refer to anything until they're defined" is meaningless, subhuman.

>>	Anonymous Mon Jan 9 19:42:32 2023 No.15111595 >>15111589 >1/9 = 0.111... >8/9 = 0.888... post proof

>>	Anonymous Mon Jan 9 19:43:40 2023 No.15111596 >>15111566 >.999... is a placeholder for a decimal expansion with an arbitrarily large natural number of digits. No.

>>	Anonymous Mon Jan 9 19:44:15 2023 No.15111598 >>15111566 > an arbitrarily large natural number of digits. Why are you moving the goal post by cherry picking natural numbers? Why not just an endless sequence?

>>	Anonymous Mon Jan 9 19:46:30 2023 No.15111603 >>15111593 LOL. Post again to demonstrate just how mentally deficient you are.

>>	Anonymous Mon Jan 9 19:48:00 2023 No.15111606 >>15111598 >he thinks he can have a non-natural number of digits go on then, show me a number with 1.5 digits.

>>	Anonymous Mon Jan 9 19:48:58 2023 No.15111607 >>15111603 Not an argument. Thanks for admitting you're subhuman.

Anonymous Mon Jan 9 19:50:45 2023 No.15111608

>>15111512
It's the definition based on decimal notation.

>>15111491
Facts and logic vs "No you're wrong"

>>15111583
Because the calculation is impossible for an infinite number there has to be another way of proving it.
There might be one but the way he did is based on unrigorous math and trying to redefine what it means to add and multiply numbers, when you mess up something learned in grade school the result you're lucky to get the right result.
If you do the same math replacing 0.999.. with the limit you won't get 1, because even though the difference between the two numbers gets closer to zero it never truly equals 0.
Or to put it simply 0.999... will never be a natural number, it will always be a real number with infinitesimal distance from the real/natural number "1".

>>	Anonymous Mon Jan 9 19:50:59 2023 No.15111609 >>15111566 >.999... is a placeholder for a decimal expansion with an arbitrarily large natural number of digits. what makes you say that?

Anonymous Mon Jan 9 19:53:33 2023 No.15111611

>>15111607
0.999... stands for the infinite sum 9/10+9/100+... which is defined as the limit of the sequence of the partial sums. In other words, it's 1 by definition. With this definition, your algebraic manipulation is a pointless tautology. Without this definition, it's meaningless nonsense. OP and others like him are questioning the definition. They don't see why an infinite sum should have any specific value since in their minds "it never gets there".

>>	Anonymous Mon Jan 9 19:54:05 2023 No.15111613 >>15111608 >It's the definition based on decimal notation. limits aren't part of the basis of decimal notation.

>>	Anonymous Mon Jan 9 19:54:10 2023 No.15111614 >>15111606 an endless sequence doesn't have a 1.5th element either. I see no problem here.

>>	Anonymous Mon Jan 9 19:54:31 2023 No.15111615 >>15111595 post disproof

Anonymous Mon Jan 9 19:56:24 2023 No.15111617

>>15111609
sequences can only have a natural number of terms. and you can have sequences with an arbitrarily large number of terms. and all natural numbers are finite. those three things together are the basis for the argument.
i hope that answers your question well enough anon.

>>	Anonymous Mon Jan 9 19:57:11 2023 No.15111619 >>15111613 Because decimal notation is used to represent fixed-length number.

Anonymous Mon Jan 9 20:01:06 2023 No.15111623

>>15111614
it also has a natural number of terms.
if you are working with a set of non-finite numbers beyond natural numbers and supposing that they exist, and can be used just as natural numbers can in certain situations, then that would be a different, new sort of decimal expansion. but its not the same one as the normal one. it would be an expansion of the natural numbers. one which is unobservable, non-measurable, and undetectable in the real world.

>>	Anonymous Mon Jan 9 20:03:20 2023 No.15111627 File: 115 KB, 600x474, 1673294584160.jpg [View same] [iqdb] [saucenao] [google] >>15111617 >sequences can only have a natural number of terms.

>>	Anonymous Mon Jan 9 20:03:35 2023 No.15111628 >>15111623 >it also has a natural number of terms. meant any sequence should have a natural number of terms.

>>	Anonymous Mon Jan 9 20:04:41 2023 No.15111630 >>15111627 post a sequence with a non-natural number of terms, like 1.5 terms or 1/2 a term then.

>>	Anonymous Mon Jan 9 20:05:27 2023 No.15111632 >>15111630 an infinite sequence

>>	Anonymous Mon Jan 9 20:06:57 2023 No.15111633 >>15111632 there's only finite sequences

>>	Anonymous Mon Jan 9 20:09:53 2023 No.15111640 >>15111617 0.999... is not a sequence though

>>	Anonymous Mon Jan 9 20:12:12 2023 No.15111644 >>15111238 I didn’t give an argument, I asked, how are you defining 0.999… ?

>>	Anonymous Mon Jan 9 20:13:47 2023 No.15111647 >>15111608 >Facts and logic vs "No you're wrong" Agreed, "0.999... doesn't make sense" is not an argument.

>>	Anonymous Mon Jan 9 20:13:47 2023 No.15111648 >>15111640 the digits can be arranged in a sequence. 9 in the 1/10ths place 9 in the 1/100ths place and so on

>>	Anonymous Mon Jan 9 20:15:45 2023 No.15111656 >>15111611 >0.999... stands for the infinite sum 9/10+9/100+... No, it's a real number which are constructed as Cauchy sequences or Dedekind cuts, not infinite sums. You don't need to do any infinite sums to prove 0.999... = 1. See >>15111402

>>	Anonymous Mon Jan 9 20:21:15 2023 No.15111672 >>15111633 Proof?

>>	Anonymous Mon Jan 9 20:25:41 2023 No.15111689 >>15111672 its just my opinion.

>>	Anonymous Mon Jan 9 20:27:11 2023 No.15111693 >>15111283 Infinitesimal

>>	Anonymous Mon Jan 9 20:32:50 2023 No.15111707 >>15111647 Define the [math] ... [/math] operator then.

>>	Anonymous Mon Jan 9 20:48:56 2023 No.15111743 >>15111707 It means "and so forth"

>>	Anonymous Mon Jan 9 20:49:57 2023 No.15111746 >>15111689 Your opinion doesn't matter in math.

Anonymous Mon Jan 9 20:54:25 2023 No.15111751

>>15111209
you see, this is actually what is Christ vs. God. Jesus is.9... God, is 1. they are both separate entities, but are equivalent. The divine mystery. Jesus will always have another 9 to complete our placeholder in the interdimensional universe, as his nines never end, but God is already whole, he is 1.

>>	Anonymous Mon Jan 9 20:55:30 2023 No.15111754 >>15111648 0.999... is not a placeholder for a sequence

>>	Anonymous Mon Jan 9 20:56:17 2023 No.15111755 >>15111746 saying infinite sequences do exist is also a opinion though anon.

>>	Anonymous Mon Jan 9 21:01:00 2023 No.15111760 >>15111751 Seems like we have a visitor from /his/

>>	Anonymous Mon Jan 9 21:07:35 2023 No.15111765 >>15111755 None of this shit exists. You assume something to be true and see where it leads. If It turns out those assumptions were useful you use them again.

>>	Anonymous Mon Jan 9 21:09:51 2023 No.15111769 >0.111... = 1/9 >0.222... = 2/9 >0.333... = 3/9 >0.444... = 4/9 And so on. Continue the pattern and you have: >0.999... = 9/9 >9/9 = 1

>>	Anonymous Mon Jan 9 21:10:42 2023 No.15111770 >division by zero NOOOOO you cant do that!! With that you can prove that 1=2 which it obviously isnt!! >infinitesimals WAOWERZ this is so useful! with this i can prove that 0.999... = 1, which obviously is true!

>>	Anonymous Mon Jan 9 21:19:31 2023 No.15111784 >>15111755 No, it's really demonstrable. The sequence of natural numbers is infinite.

>>	Anonymous Mon Jan 9 21:21:11 2023 No.15111785 >>15111770 Where were infinitesimal used for this proof? >>15111402

>>	Anonymous Mon Jan 9 21:25:09 2023 No.15111790 >>15111785 Do you know the definition of dedekind cuts? Pick up a book in real analysis, i recommend Rudin's principles of mathematical analysis.

>>	Anonymous Mon Jan 9 21:27:15 2023 No.15111793 File: 88 KB, 1024x512, FOffBWwaUAA0Z5j.jpg [View same] [iqdb] [saucenao] [google] >>15111790 Damn bro you just memorize definitions with no understanding

>>	Anonymous Mon Jan 9 21:35:29 2023 No.15111817 0.999... isn't equal to 1 because 0.999... doesn't exist.

>>	Anonymous Mon Jan 9 21:36:30 2023 No.15111822 >>15111770 >division by zero...you can't do that!!! >division by infinity? that's A-okay!

>>	Anonymous Mon Jan 9 21:37:38 2023 No.15111823 File: 7 KB, 233x216, b96bcd77d412a4aaeadb8d0f39ae8661.jpg [View same] [iqdb] [saucenao] [google] >>15111817 But what if it did tho

>>	Anonymous Mon Jan 9 21:37:43 2023 No.15111825 File: 473 KB, 704x659, 19684064823.png [View same] [iqdb] [saucenao] [google] >>15111793 You dont seem to understand dedekind cuts or infinitesimals so you're clearly out of your depth

>>	Anonymous Mon Jan 9 21:41:41 2023 No.15111832 >>15111790 I do, what don't you understand about my proof?

>>	Anonymous Mon Jan 9 21:44:40 2023 No.15111839 >>15111832 >spoon-feed me Read your "proof" again and then read real analysis again, not everything is going to be handed to you on a silver platter in life

>>	Anonymous Mon Jan 9 21:45:36 2023 No.15111842 >>15111817 But algorithms exist, and you can write an algorithm to give a rational approximation to within any desired precision

>>	Anonymous Mon Jan 9 21:47:08 2023 No.15111845 this thread is basically a philosophy of mathematics thread. don't think these problems will be ironed out any time soon.

>>	Anonymous Mon Jan 9 21:48:47 2023 No.15111851 >>15111845 This is a grade school equality

>>	Anonymous Mon Jan 9 21:50:40 2023 No.15111864 1-0.9=0.1 1-0.99=0.11 1-0.999=0.111 ... 1-0.999999999... = 0.1111111111..... which clearly isnt zero. Sometimes i wonder if all of you are just a bunch of seventh graders

>>	Anonymous Mon Jan 9 21:51:30 2023 No.15111866 >>15111839 OK, so there is nothing wrong with the proof and you're just whining. Thanks for admitting that.

>>	Anonymous Mon Jan 9 21:54:03 2023 No.15111884 they are only represented differently

>>	Anonymous Mon Jan 9 21:54:22 2023 No.15111885 >>15111864 1-1=0 1-1.0=0 1-1.00= 0

>>	Anonymous Mon Jan 9 21:59:43 2023 No.15111908 >>15111866 I accept your concession

>>	Anonymous Mon Jan 9 22:03:00 2023 No.15111920 >>15111864 >1-0.999999999... = 0.1111111111..... No it doesn't [math]1-0.9=0.1[/math] [math]0.1-0.09=0.01[/math] [math]1-0.999...=0.000...[/math]

>>	Anonymous Mon Jan 9 22:10:47 2023 No.15111941 >>15111851 do you happen to think grade school maths is rigourous

>>	Anonymous Mon Jan 9 22:32:34 2023 No.15111996 >>15111908 Of what? You're the one who stopped arguing.

>>	Anonymous Mon Jan 9 22:34:56 2023 No.15111999 >>15111941 You're right, 1+1=2 is unrigorous.

>>	Anonymous Mon Jan 9 22:38:14 2023 No.15112004 >>15111999 yeah, you'd need to read principia mathematica for it to be rigorous.

>>	Anonymous Mon Jan 9 22:41:12 2023 No.15112008 >>15111209 >without algebra im gonna do it brah let's say a=0.999999999999999999..... 10a=9.9999999999999.... so 10a-9=0.999999999999999999..... which means 10a-9=a so we get 10a-a=9 9*a=9 a=1

>>	Anonymous Mon Jan 9 22:42:28 2023 No.15112011 >>15111920 i think you didn't even pass high-school at least for now am i wrong ?

>>	Anonymous Mon Jan 9 22:42:46 2023 No.15112012 >>15111743 Define it in terms of operations on numbers. And so forth could mean the 9s end at some point because in the case of any real world measurement that's what would happen.

>>	Anonymous Mon Jan 9 22:44:12 2023 No.15112016 >>15111864 >1-0.9999...=0.1111.. The fuck you are dumb Does in your shithole country exist something named "calculator" ? Use it and see

Anonymous Mon Jan 9 22:47:04 2023 No.15112026

>>15111647
if 0.9999... is a number which makes sense according to you then i dare you to add it to 3 and write the result

you won't be able to write it so the number itself doesn't make sense because it's not a number it's a representation of the infinitesimal difference applied to 1

>>	Anonymous Mon Jan 9 22:48:31 2023 No.15112033 keep adding 9's forever and eventually it just becomes 1, simple as.

>>	Anonymous Mon Jan 9 22:52:04 2023 No.15112040 >>15112033 You can't reach forever. That's why there's limits

>>	Anonymous Mon Jan 9 22:53:03 2023 No.15112041 >>15111279 You can't put another 9 at the end of it, the "..." means it goes on forever.

>>	Anonymous Mon Jan 9 22:55:42 2023 No.15112050 File: 65 KB, 540x959, NINTCHDBPICT000706430807.jpg [View same] [iqdb] [saucenao] [google] >>15111864 1% of 1 is eleven hundredths

>>	Anonymous Mon Jan 9 22:57:24 2023 No.15112056 >>15112041 Yes, so it's any number between 0.9 and 0.999... Doesn't matter how many 9-s you put there, it's still not 1

>>	Anonymous Mon Jan 9 22:59:27 2023 No.15112061 >>15112056 Again, it goes on forever. No matter how far you went you'd find more 9s. You're not putting on any particular number of 9s.

>>	Anonymous Mon Jan 9 23:01:03 2023 No.15112065 >>15111276 Yes actually. 0.999... + 0.000...

>>	Anonymous Mon Jan 9 23:08:58 2023 No.15112080 >>15112011 >am i wrong ? Yes. I am actually a professor of mathematics at Cambridge.

>>	Anonymous Mon Jan 9 23:12:05 2023 No.15112093 >>15112056 Name a number between 0.999… and 1

>>	Anonymous Mon Jan 9 23:18:10 2023 No.15112113 >>15112061 It's an infinite set of finite numbers

>>	Anonymous Mon Jan 9 23:23:04 2023 No.15112129 >>15112113 It's a single number, whose written form continues infinitely.

>>	Anonymous Mon Jan 9 23:24:02 2023 No.15112132 >>15111342 I love how he blew their arguments out of the water and they’re left seething in shambles

>>	Anonymous Mon Jan 9 23:27:49 2023 No.15112149 >>15111209 >Prove 0.99... = 1. >and DON'T use mathematics. Give me a real answer.

>>	Anonymous Mon Jan 9 23:28:29 2023 No.15112155 >>15111209 Floating point is fake and gay. QED.

>>	Anonymous Mon Jan 9 23:32:02 2023 No.15112164 >>15112129 So it's any number with any amount of 9-s in it, ergo an infinite set of numbers

>>	Anonymous Mon Jan 9 23:34:34 2023 No.15112173 >>15112164 No, it's the number in which the 9s go on forever. As in, if you look at the nth digit, for any value of n however large, it will be 9.

>>	Anonymous Mon Jan 9 23:37:42 2023 No.15112178 File: 306 KB, 1128x480, 15fea505-1e96-42fb-be44-131804fb13b3_screenshot.png [View same] [iqdb] [saucenao] [google] >>15111209 >why isn't it bigger than one >it just isn't >why not, you stupid bastard

>>	Anonymous Mon Jan 9 23:42:30 2023 No.15112187 File: 223 KB, 1292x682, The Outer Limits of Reason - The outer limits of reason what science mathematics and logic cannot tell us .png [View same] [iqdb] [saucenao] [google] >>15111209 >HOW CAN IT BE 1? It can't be. As stated in pic related.

>>	Anonymous Mon Jan 9 23:44:49 2023 No.15112192 >>15112026 3.9999...

>>	Anonymous Mon Jan 9 23:53:50 2023 No.15112228 >>15112041 Oh? So what is pi then? 3.1415159265... ? 3.1415...? 3.14...? 3....? ... ?

>>	Anonymous Mon Jan 9 23:55:22 2023 No.15112233 >>15112093 0.999 + nigger where nigger is the half the difference between 1 and 0.999...

>>	Anonymous Mon Jan 9 23:56:31 2023 No.15112241 >>15112187 limit cultists won't like this one

>>	Anonymous Mon Jan 9 23:58:51 2023 No.15112246 >>15112228 What kind of question is that? It's irrational.

>>	Anonymous Tue Jan 10 00:00:43 2023 No.15112252 >>15112173 Yes, so it's an infinite set of numbers

>>	Anonymous Tue Jan 10 00:03:19 2023 No.15112259 >>15112252 It is a particular number, or rather a particular representation of a number, which contains an infinite number of digits.

>>	Anonymous Tue Jan 10 00:06:06 2023 No.15112265 >>15111209 >it literally says "arbor" how can that BE "tree"

>>	Anonymous Tue Jan 10 00:08:57 2023 No.15112273 >>15112259 So it can be any number with any amount of digits that falls within that infinite set of numbers

Anonymous Tue Jan 10 00:09:02 2023 No.15112275
File: 3.41 MB, 2052x1184, tom Campbell computing reality.png [View same] [iqdb] [saucenao] [google]

>>15112241
True. People that believe in physical countinuousness won't like it either. The physical world is discrete/digital (computable/informational).

>>	Anonymous Tue Jan 10 00:12:17 2023 No.15112284 >>15112273 No. It is not 0 with a million 9s, or a billion 9s, or a googolplex 9s, but 0 with an infinite number of nines.

>>	Anonymous Tue Jan 10 00:15:03 2023 No.15112289 >>15112284 So any amount of 9s, got it

>>	Anonymous Tue Jan 10 00:16:56 2023 No.15112293 >>15112289 No, "infinity" and "any amount" are not the same. 0.9999... is the number with the property that no matter what digit of it you look at, it will always be a 9.

Anonymous Tue Jan 10 00:20:40 2023 No.15112301
File: 134 KB, 496x496, 1595871990984.jpg [View same] [iqdb] [saucenao] [google]

>>15112293
>0.9999... is the number with the property that no matter what digit of it you look at, it will always be a 9.
But there's a 0 in it, you're not very good at math, are you?

>>	Anonymous Tue Jan 10 00:32:16 2023 No.15112325 >>15111372 each line is exactly =1/3 it's your job to show where it suddenly starts diverging from that

>>	Anonymous Tue Jan 10 00:34:13 2023 No.15112328 friendly reminder that you may not assume that 1/3 = 0.999.... since 0.99.... is irrational

>>	Anonymous Tue Jan 10 00:34:16 2023 No.15112330 >>15112301 You know what I mean. Any digit after the decimal point.

>>	Anonymous Tue Jan 10 00:35:39 2023 No.15112333 >>15112330 Still doesn't make you any less wrong

>>	Anonymous Tue Jan 10 00:36:37 2023 No.15112336 >>15112333 You are either a troll or stupid and I'm not sure why I'm still responding to you.

>>	Anonymous Tue Jan 10 00:39:52 2023 No.15112341 >>15112328 >t. friendly idiot not one but TWO mistakes, lol

>>	Anonymous Tue Jan 10 00:41:06 2023 No.15112342 >>15112336 >I'm not sure why I'm still responding to you. Because you can't accept that you are wrong

>>	Anonymous Tue Jan 10 00:44:18 2023 No.15112349 >>15112341 ad hominem

>>	Anonymous Tue Jan 10 00:56:12 2023 No.15112371 >>15112349 nah, that would be argumenting just based on your idiocy. i'm criticizing you based on fitting two mistakes in a short sentence. the rest is just being impolite, not AH

>>	Anonymous Tue Jan 10 01:18:06 2023 No.15112393 >>15112065 In terms of limits [math] \lim \sum_{k=1}^{n} \frac{9}{10^k} + \lim \frac{1}{10^{n+1}} [/math]

>>	Anonymous Tue Jan 10 02:06:09 2023 No.15112462 >>15112393 >In terms of limits

>>	Anonymous Tue Jan 10 02:19:16 2023 No.15112479 0.9... is a recursive function with zero computational time. If it had a small amount of computational time it would never reach 1. But since it is computed instantly you can simply say that it doesn't equal 1.

>>	Anonymous Tue Jan 10 03:24:03 2023 No.15112573 >>15112012 >Define it in terms of operations on numbers. Why? It's not an operation. >And so forth could mean the 9s end at some point No. >because in the case of any real world measurement Irrelevant.

>>	Anonymous Tue Jan 10 03:34:11 2023 No.15112598 File: 111 KB, 953x613, wNQjUVS.jpg [View same] [iqdb] [saucenao] [google] >>15111209 OP is retarded. Here we go again...

>>	Anonymous Tue Jan 10 03:40:24 2023 No.15112605 1/3 = 0.333... 1/3 2/3 = 0.666... 4/6 3/3 = 0.999... 9/9

>>	Anonymous Tue Jan 10 03:40:37 2023 No.15112607 >>15112012 >could mean the 9s end at some point No. They categorically go on forever. When you run the math, 0.999.. is, -precisely- 1.

>>	Anonymous Tue Jan 10 04:50:20 2023 No.15112707 File: 1.46 MB, 498x379, 1670795969087208.gif [View same] [iqdb] [saucenao] [google] >>15112598 >1=0.999...

>>	Anonymous Tue Jan 10 05:49:42 2023 No.15112859 >>15111209 It's not 1. It clearly shows that it's not.

>>	Anonymous Tue Jan 10 05:51:34 2023 No.15112861 >>15112598 Retarded proofs for retarded poster. Good job.

>>	Anonymous Tue Jan 10 05:53:05 2023 No.15112863 >>15112598 I'm not sure why he claimed infinitely small numbers don't exist. Abraham Robinson created a rigorous framework for infinitesimals.

>>	Anonymous Tue Jan 10 08:59:12 2023 No.15113076 >>15111277 Then if we call your assumption x, what is the difference between 1 and x, ie what is the value of 1-x?

>>	Anonymous Tue Jan 10 14:00:17 2023 No.15113331 >>15112598 >circle arguments yawn

>>	Aether king of sci Tue Jan 10 14:23:49 2023 No.15113350 File: 28 KB, 600x600, 1671885974674360.jpg [View same] [iqdb] [saucenao] [google] 0.075 proves 1 isn't the lowest unit. There is '~' which symbolizes a logical quart. 0.99999 does equal 1 but it's a retard error in base system.

>>	Anonymous Tue Jan 10 16:09:07 2023 No.15113460 >>15111315 1/3 is not equal to 0.333333333... Under the base 10 system, dividing 10^x by 3 gives you an infinitely recurring decimal. It's impossible to represent 1/3 as a decimal number. You must use fractions.

>>	Anonymous Tue Jan 10 16:11:46 2023 No.15113466 It's not 1 It's always a hair width away from 1 But the limit of it approaches to 1

>>	Anonymous Tue Jan 10 16:13:32 2023 No.15113471 >>15113460 That's what the "..." means- infinitely recurring decimal.

>>	Anonymous Tue Jan 10 16:16:17 2023 No.15113475 >>15111209 > 1/3 = 0.33333... > 3 * 1/3 = 3 * 0.33333... > 3/3 = 0.99999... Since 3/3 = 1, 1 = 0.99999... No algebra

>>	Anonymous Tue Jan 10 16:18:38 2023 No.15113480 >>15113475 That's literally algebra

>>	Anonymous Tue Jan 10 16:21:04 2023 No.15113485 >>15111442 You're being retarded. Don't you know what happens when you multiply 999999 by 9? You can't just slap an extra 9 onto the end. This is grade school math, dipshit.

Anonymous Tue Jan 10 16:22:45 2023 No.15113490

>>15111321
> Step 1: 1/3, how many times does 3 fit in 1? Zero
> What's left over? One.
> Alright, since we still have stuff left let's move on
> Step 2: 10/3, how many times does 3 fit in 10? Three!
> What is the extra? One.
> Alright, since we have stuff left let's move on.

Repeat step 2 forever.
Each step is one decimal.
So 0.333... repeating 3s infinite times.

>>	Anonymous Tue Jan 10 16:26:22 2023 No.15113494 >>15113490 so that means there's always a remainder. so it would be .333... and a non-zero remainder based on how many 3s you calculated to.

>>	Anonymous Tue Jan 10 16:26:24 2023 No.15113495 >>15113471 1/3 cannot be written as a decimal. You can only get infinitesimally close to the value of 1/3. Simple as.

>>	Anonymous Tue Jan 10 16:27:05 2023 No.15113496 x = 0.99999......9 1-x = 0.00000...1 = dx dx is so small with infinite zeroes that it literally becomes zero

>>	Anonymous Tue Jan 10 16:27:39 2023 No.15113497 >>15113495 Yes, it's infinitely recurring so you can't write it out in full, that's what the "..." means.

>>	Anonymous Tue Jan 10 16:30:20 2023 No.15113500 >>15111519 Infinity can be a tough concept to grasp There is no empty space, only nines. All the way down.

>>	Anonymous Tue Jan 10 16:31:14 2023 No.15113501 >>15113496 >dx is 0 that will simplify my integral calculations a bit

>>	Anonymous Tue Jan 10 16:35:08 2023 No.15113506 >>15111623 How many halfwaypoints does your hands have to pass to clap together? Do they ever reach each other?

>>	Anonymous Tue Jan 10 16:37:18 2023 No.15113509 >>15111633 What is the biggest number?

>>	Anonymous Tue Jan 10 16:38:33 2023 No.15113511 >>15113485 >Don't you know what happens when you multiply 999999 by 9? Where is that in the argument? Retard.

>>	Anonymous Tue Jan 10 16:41:56 2023 No.15113516 >>15112008 That's a nice proof I like this proof

>>	Anonymous Tue Jan 10 16:43:08 2023 No.15113519 >>15112026 4

>>	Anonymous Tue Jan 10 16:46:12 2023 No.15113522 >>15111209 >1-0.999... = ? >0.999... - 1 = ? I know none of you midwits will answer.

>>	Anonymous Tue Jan 10 16:47:23 2023 No.15113526 >>15113522 they are infinitesimals

>>	Anonymous Tue Jan 10 16:48:23 2023 No.15113530 >>15113522 >>1-0.999... = ? >>0.999... - 1 = ? ...1 and ...-1 next

Anonymous Tue Jan 10 16:49:59 2023 No.15113533
File: 533 KB, 2434x1512, universe creation bwhit .png [View same] [iqdb] [saucenao] [google]

>>15112598
You can't put exactly 1/3 water in each glass to an infinite amount of decimal places. This is an idealistic, non -physical procedure. Matter is quantized and so there would not be the same amount in each. There would be a positive natural number for each minimal finite element. There are no infinite anything in the physical world. No infinite divisibility, no continuousness, no analyticity. None of that. see here
>>15112275
This is why everything blows up when you try and go below the planck length by the way. It's a processor overload. It's pixelated down there.
You confuse the math model with the physical reality. These continuous math models have utility because the planck length, for instance, is so small that the models make useful predictions down to a non--arbitrary resolution and limited decimal places. There is a minimal delta t of time as well, see pic.
And none of this infinite/continuous/analytic stuff could ever be verified either using measurements upon the experiential/sensual datastream, ie it could not be confirmed empirically. This is a metaphysical claim. I am fine with this myself, being that I am an idealist and platonist and not an empiricist, and I don't believe that the physical world is fundamental, but derivative, so this infinite/continuous/analytic stuff could be grounded in mind, the all mind, god, platonic realm, whatever you want to call it, but it's not physical.

>>	Anonymous Tue Jan 10 16:51:38 2023 No.15113537 File: 163 KB, 1612x578, bwhitworthquantreal pix cycles.png [View same] [iqdb] [saucenao] [google] >>15112598 Wrong pic related here >>15113533 should be pic related

>>	Anonymous Tue Jan 10 16:54:50 2023 No.15113539 >>15113533 Yes in reality there is no infinites But we're discussing math. Not reality aren't we?

>>	Anonymous Tue Jan 10 16:59:08 2023 No.15113548 >>15113539 Universe is infinitely long and small

>>	Anonymous Tue Jan 10 17:00:51 2023 No.15113553 >>15113548 We don't know that Just a decent guess

Anonymous Tue Jan 10 17:36:24 2023 No.15113600

>>15113539
I think you should start by defining 'reality'. A discussion about what 'is' or what is 'real' is a meta physical (ontological) discussion, not a scientific/empirical one. I myself do not think the (effectively) objective (I say effectively because of recent verifications of wigner's friend type thought experiments) datastream called the physical world is the only reality. I don't believe that a physicalist metaphysical viewpoint can account for things like consciousness, identity over time, the invariant across space and time nature of number, and all kinds of other universals. So I don't believe that math is necessarily fake or not 'real' just because it is not physical. My main point for posting that post was from a position of PHYSICAL finitism. On Mathematical finitism I will admit to being agnostic at this point. This is why I like these threads. I look at the subject matter open mind. This is why I watch the shit out of Norman J. Wildberger vids as well. such as this
https://www.youtube.com/watch?v=fCZ8jJCVinU
He is, of course, a physical AND math finitist or ultra-finitist or maybe even a double mega omni finitist. He definitely is an empiricist with regard to math, but I don't think he realizes that this in itself is a metaphysical (ontological) position, and so it in itself can not be verified by the scientific method or the subjective sensual datastream that gets somehow beamed into our mind to experience, that we call the 'objective' physical world. He was pushed back a bit about this in this interview.
https://www.youtube.com/watch?v=l7LvgvunVCM
I don't know the time stamp but it is there somewhere.

>>	Anonymous Tue Jan 10 17:44:07 2023 No.15113613 >220 posts about 0.999... did I timeslip back into 2014

Anonymous Tue Jan 10 17:51:42 2023 No.15113627

>>15113600
You use too many flowery words to describe sollipsism.

Math is useful. It has practical purpose.
Reality is real enough, wether infinite or not.

Things are never perfect, or 100%
Just good enough.
Close enough to 1 to be 1 for all purposes.

Anonymous Tue Jan 10 18:08:47 2023 No.15113658

>>15113627
>You use too many flowery words to describe sollipsism
This is not really an argument against anything I said. Sounds like you are approaching an argument from and appeal to consequence. See pic. I am not asserting that metaphysical solipsism is true. I didn't even mention solipsism. Epistemic solipsism, though, is just a brute fact that any world view has to deal with. Do you have access to someone ELSE'S sensual datastream of the physical world? I don't.
>Math is useful. It has practical purpose.
Yes
>Reality is real enough, wether infinite or not
You still didn't define 'reality'. Certainly the physical data stream that our mind is presented with is real enough to achieve the VR concepts of immersion and presence. More immersive that the dream datastream in terms of being more persistent.

>>	Anonymous Tue Jan 10 18:10:32 2023 No.15113661 File: 56 KB, 1285x214, appeal to consequence .png [View same] [iqdb] [saucenao] [google] >>15113627 Forgot pic here >>15113658 see pic

Anonymous Tue Jan 10 18:21:56 2023 No.15113684
File: 3 KB, 305x165, download.png [View same] [iqdb] [saucenao] [google]

>>15111209
ok. Assuming your graphic description is an infinite amount of zeros, one can define this as being the sum in picrel.
the sum of (q)^n with n going to infinity for a converging sum (this is obviously converging) is 1/(1-1/10) *9 (the nine in front of the sum) but the sequence also has to include the 0th term which is 9. By plugging in 1/10 and substracting you get 1.

Simply put, 0.99999 is the (converging) sum of a sequence and by taking it to infinity, you're basically saying it's equal to one.

There you go. It's surprising I didn't see this answer in this 200+ reply long thread.

>>	Anonymous Tue Jan 10 18:33:07 2023 No.15113710 >>15113658 Oh, no sorry Didn't mean it as an argument It's just an opinion Sorry about that misunderstanding I should have added "...for my liking" at the end. It is mostly because I am tired I said it.

Anonymous Tue Jan 10 18:40:02 2023 No.15113733

>>15113658
When it comes to the age old "Am I a man dreaming he is a butterfly or a butterfly dreaming it is a man" question. My personal response is that either way things are the same. And either way you're best off assuming whatever reality you're currently in to be real.

"Pain's just chemicals in the brain" and all. It's still pain, it's still useful.

The input that our globs of brain matters gets from the world is all it has. Sure we're technically globs trapped in the dark inside a suit of bone and flesh who never experience anything directly.

Yet your mind and my mind are connecting with each other, sharing thoughts. Imperfectly sure but it's still quite the feat and ignoring it, or dismissing the idea that it might be real, really is missing out a whole lot on simply existing.

Anyway, back to math.

>>	Anonymous Tue Jan 10 18:48:16 2023 No.15113755 >>15113710 > No problem. No offence taken. >>15113733 I don't really see that much to argue over in your post so I won't. Enjoy the math.

>>	Anonymous Tue Jan 10 18:54:01 2023 No.15113776 >>15113755 Thank you Hope you enjoy yourself too

Anonymous Tue Jan 10 19:00:35 2023 No.15113790
File: 324 KB, 882x889, NJW.png [View same] [iqdb] [saucenao] [google]

>>15111427
This isn't proof. Why? Because there is no reason to assume that arithmetic is well-defined for these infinite decimals or even that this object even exists in any reasonable form. Moreover, the pattern of the listed digits needs to represent the pattern of the digits alleged to exist by "..." as those digits may be calculated by a different algorithm from the the one used to calculate the listed digits or the algorithm used to the generate 0.9999...* just results in the first four digits being 9's while who knows whatever the "rest" of the digits are. Of course, you really can't calculate them all. Second, there is no reason to believe that such the expression 0.9999... actually represents anything meaningful.
>>15113500
>Infinity can be a tough concept to grasp
Infinity is not rigorously defined here and in most circumstances such as this one, it never is well-defined. Moreover, there is no reason to assume
>There is no empty space, only nines
even after multiplying the alleged object as it is entirely unclear whether or not the arithmetic can really be defined given the law of logical honesty. If we're playing this infinity game, then why can't I add 0 to the infinity + 1 slot then and follow the usual rules of arithmetic by 10? There is no reason why I shouldn't be able to from this choice perspective appealed to with these infinite objects. There are an infinite number of digits, but the last one is 0.

>>	Anonymous Tue Jan 10 19:13:43 2023 No.15113815 >>15111209 1/3 = 0.33333333... and 3*1/3 =1 therefore 0.99999... = 1 at this point if you don't understand this the word retard doesn't even describe you

>>	Anonymous Tue Jan 10 19:14:22 2023 No.15113818 >>15113790 There is no infinity+1 slot Infinity + 1 is still just infinity. Per definition, infinite means without end. So there's a 9 in the way

Anonymous Tue Jan 10 19:16:23 2023 No.15113826
File: 62 KB, 1280x720, maxresdefault-3490073748.jpg [View same] [iqdb] [saucenao] [google]

>>15111595
Easy :

1/9 = 100/900 = (90 + 10)/(9*100)
1/9 = 90/900 + 10/900
1/9 = 1/10 + 1/90

But...
1/90 = 100/9000 = (90 + 10)/(9*1000)
1/90 = 90/9000 + 10/9000
1/90 = 1/100 + 1/900

Etc. for 1/9000, 1/90000, etc.

Then :
1/9 = 1/10 + 1/100 + 1/1000 + ....
1/9 = 0,1111111....

>>	Anonymous Tue Jan 10 19:20:10 2023 No.15113831 >>15112246 i say, imagine...

Anonymous Tue Jan 10 19:42:42 2023 No.15113873
File: 663 KB, 1421x957, NJWW.png [View same] [iqdb] [saucenao] [google]

>>15113818
>There is no infinity+1 slot
Not according to modern analysis. Especially when you can just write something like [math] [0,1] \equiv [-\infty, \infty] [/math]. I can simply add a point at the end, call it [math] \infty +1 [/math], noting that since [math]\infty+1 > \infty[/math]. It is consistent with assertions of set theory. Moreover its consistent with analysis
>Infinity + 1 is still just infinity.
There is no reason to assume any such arithmetic here either.
>Per definition, infinite means without end.
Infinite is most clearly defined as "non-finite." However, finite itself is not well-defined either outside of perhaps saying that you can assign a natural number to specify specific elements of an "object" whether its the number of elements in a list or the amount of marbles in a box. "Infinite" in these contexts is solely the negation in these examples of what someone might mean by "finite" that you cannot assign a natural number to the amount of elements of a list or marbles in a box. As such it is logically invalid to assume there is such a number or quantity called [math] \infty [/math] or to speak about properties of this thing when it only exists as a logical negation of a very specific property. Either you can do something, or you can't. Finite means you can do something "infinite" only means you can't do that thing.

>So there's a 9 in the way
Except there isn't as before, I showed that according to modern set theory and the axiom of choice we can introduce a unique object called [math] \infty+1 [/math] to the natural/real number line which is greater than [math] \infty [/math] which leads to a 9 in the [math] \infty +1 [/math] place of the number. Hence when we multiply by 10, we move the [math] \infty +1 [/math] 9's up a decimal place so that the [math] 9 [/math] is in the [math] \infty th [/math] decimal place while now we write [math] 0 [/math] in the [math] \infty + 1 [/math] decimal place.

Anonymous Tue Jan 10 19:50:48 2023 No.15113892

>>15113873
By definition, infinity + 1 equals infinity
It is bigger than the biggest number.
In fact, it isn't a number at all. It is literally everything, the set of sets.

Just like there is no biggest number, there is no end to the nines. That's what the three dots represent.

Infinity is not finite, not constrained. It has no end. It can't be treated like a number.

>>	Anonymous Tue Jan 10 19:54:24 2023 No.15113902 >>15113892 >there is no end to the nines. 0,999999... >there is a 9 at infinity. 0,99999...9 Not the first Anon, but here is his mental gymnastic he cant do : Both are the same. 0,99999...9 = 0,999999...

>>	Anonymous Tue Jan 10 19:55:36 2023 No.15113907 >>15113902 Those are not the same One is finite, the other is infinite

>>	Anonymous Tue Jan 10 19:57:25 2023 No.15113916 >>15113902 There exists no point that is infinity. It isn't a place that can be reached. Just like there exists no biggest number.

>>	Anonymous Tue Jan 10 19:58:16 2023 No.15113918 >>15113907 >One is finite Hmmm... which 1 ?

Anonymous Tue Jan 10 20:01:04 2023 No.15113935

>>15113918
The one that has an end.

Infinity isn't a number. Which is exactly why 0.999... is just a different way of writing 1.0

There is nothing to separate them, infinite nines leaves no possible space for anything to be placed inbetween them. To separate them

>>	Anonymous Tue Jan 10 20:05:17 2023 No.15113950 >>15113935 There simply exists no way to tell them apart. They are completely identical

>>	Anonymous Tue Jan 10 20:07:49 2023 No.15113954 >>15113935 >The one that has an end. ...at infinity. Dont know for you, but for me, something that has an end at infinity is literally infinite by definition.

>>	Anonymous Tue Jan 10 20:09:04 2023 No.15113957 >>15113918 >which 1 ? Subtle :)

>>	Anonymous Tue Jan 10 20:09:19 2023 No.15113959 File: 185 KB, 835x893, 1649880599985.png [View same] [iqdb] [saucenao] [google] >>15111209 >Prove it robustly without a bunch of algebra

Anonymous Tue Jan 10 20:11:26 2023 No.15113966

>>15113954
You can never reach infinity

It's why 0.000... doesn't work. Like this it's just zeroes nothing else. And that's just 0.
But if you add a 1 at the *end*

0.000...01, suddenly you don't have enough zeroes! I can just keep adding nines forever. Running away from the one. Infinity can't end, per definition. There exists no infinitieth point on the chain because if you can add something new beyond it, then it wasn't infinite.

Anonymous Tue Jan 10 20:15:09 2023 No.15113974

>>15113892
>By definition, infinity + 1 equals infinity
Nope. It doesn't.
>It is bigger than the biggest number.
There is no such thing as a number called infinity, hence it cannot be compared to any other number. However, assuming such a thing
>In fact, it isn't a number at all. It is literally everything, the set of sets.
The idea of a "set of sets" or ever further, a "set of all sets" which would be what is typically asserted as a maximal element in these set theoretic concerns and the analytic concerns when one approaches the extended real number line [math] [-\infty, \infty] [/math] leads to the Russel paradox. The Russel paradox would rather imply that there is no such thing as an infinity as it would be as asserted here, be the maximal set containing all sets, yet cannot contain itself else it would not be maximal.

The fundamental problem here on your part as well as modern math is a sever misunderstanding of foundational concerns. You CANNOT assert there is such an object called infinite or that one can create such an object that has an "infinite" number of elements or anything else along those lines. The fact that you cannot assign a natural number to the total number of natural numbers for example does not imply there is such thing as an infinite. A negation of a positive statement does not posit the existence of an object.
>Just like there is no biggest number, there is no end to the nines. That's what the three dots represent.
And that infinite is bounded as the assertion [math] [0,\infty] \equiv [0,1] [/math] implies. So there is 0.9...9 and the dots represent an infinite number of 9's between the first and [math] \infty[/math]th decimal place.

>>	Anonymous Tue Jan 10 20:19:47 2023 No.15113984 >>15113974 Kinda showcases that math is imperfect doesn't it? And can't adequately be used to represent everything

Anonymous Tue Jan 10 20:23:17 2023 No.15113994
File: 97 KB, 720x540, NJW.jpg [View same] [iqdb] [saucenao] [google]

>Infinity is not finite,
Again, the ability to assert that there is a logical negation of a term i.e. finite is negated by infinite/non-finite. Does not imply the existence of a number called infinity and is not justification of such a thing. Rather paradoxes like the Russel Paradox or various other paradoxes derived from modern set theory like the Banach-Tarski paradox prove there logically cannot be objects as assuming their existence leads to blatant logical contradictions.

Finite only means that a natural number can be assigned to the quantity of objects of a certain type in this context. Infinite, being the negation implies that a finite-number cannot be assigned a natural number. The fact that there is a negation again does not imply the exist of an object called infinity. It does not imply anything like
>not constrained
>It has no end.
as you are positing. At best, it means that an additional digit or an additional element can be added
>It can't be treated like a number.
Rather there is no such thing as an object called infinity in this context. Plain and simple.
>>15113984
Absolutely. Much of modern math is a shellgame.

>>	Anonymous Tue Jan 10 20:31:35 2023 No.15114015 >>15113994 Woah woah woah I never claimed there to exist a number called infinity. It's not an object. Thinking of it like one is part of the issue you're having I think. You're probably better off thinking of it as a limit.

Anonymous Tue Jan 10 20:49:37 2023 No.15114059

>>15114015
>It's not an object.
There is no such thing as infinity.
>Thinking of it like one is part of the issue you're having I think.
The problem's are on your part because there is no such thing as infinity yet you keep trying to pretend there is or using the term in some loosy-goosy undefined fashion. Then when push comes to shove you try to move the goalposts and change what you mean
>You're probably better off thinking of it as a limit.
As if I'm supposed now treat this on the same footing as limits like 0 as the limit to a sequence [math] x_n = 1/n [/math] or as an upper bound like [math] 1 [/math] is to the set [math] [0,1] [/math]. In which case you're tell me to treat it as a mathematical object. Yet then you say it's not an object. Do you even realize the contradictions you're spouting? Either its a mathematical object or it has no place in mathematics as it cannot described in terms of mathematical objects. You've already claimed that it's a "set of all sets" in which case it would be a mathematical object as a set is supposed to be a mathematical object in Cantor or ZFC set theory.

Anonymous Tue Jan 10 20:53:42 2023 No.15114066

>>15114059
Infinity is simply a representation of something never ending.

0.999... has no last 9 and no more numbers can be added to it. It's what 0.999... means.

If you don't want to wrap your head around something that does not end. Eh, be my guest I suppose.

>>	Anonymous Tue Jan 10 21:01:06 2023 No.15114082 >>15113494 Remainders only exist in integer arithmetic. For rational numbers, remainders don't exist.

>>	Anonymous Tue Jan 10 21:16:35 2023 No.15114124 >>15114059 What's the cardinality of the set containing all real numbers?

>>	Anonymous Tue Jan 10 22:23:19 2023 No.15114325 >>15113522 0.00.. and then a 1 -0.00... and then a 1

>>	Anonymous Tue Jan 10 22:24:17 2023 No.15114327 >>15114325 You never reach the one You need more zeroes

>>	Anonymous Tue Jan 10 22:25:57 2023 No.15114334 >>15114327 you do. you can literally see the 1s there

Anonymous Tue Jan 10 22:36:34 2023 No.15114361

>>15114334
If you can see the one you haven't gone far enough.

See, let's rake this a step at a time

1 - 0.9 = 0.1 right? But whoops there was another nine there we missed. Silly us
So it's actually 1 - 0.99 = 0.01 ah but shoot, missed yet another nine!

And so on. There is no end to the nines, they will keep running away from you and you will never reach the solution you're after. You'll never reach the final one, it doesn't exist.

>>	Anonymous Tue Jan 10 23:03:00 2023 No.15114408 >>15114361 but if somehow this calculation did take place: 1 - 0.999... = what would the result be

>>	Anonymous Tue Jan 10 23:10:52 2023 No.15114436 >>15114408 0 obviously since 1=0.999...

Anonymous Tue Jan 10 23:13:50 2023 No.15114449

.999... does not exist, infinity is not actually a real number.

But as .999 increases, the value infinitely approaches 1, so that's why it's considered to be 1, that's the limit...

For example
1 - 0.9 = 0.1.
1 - 0.99 = 0.01
1 - 0.999 = 0.001

The pattern keeps repeating as the difference between 1 and 0.999... approaches ZERO. So the limit of 0.999...n... as it approaches infinity is 1.

Now go to bed.

Anonymous Tue Jan 10 23:23:53 2023 No.15114466

[math] x = 0.999... [/math]
[math] x = \lim_{n\rightarrow \infty} \sum_{k=1}^{n} \frac{9}{10^k}[/math]
[math] 10x = 10 \times \lim_{n\rightarrow \infty} \sum_{k=1}^{n} \frac{9}{10^k} [/math]
[math] 10x = \lim_{n\rightarrow \infty} 10 \times \sum_{k=1}^{n} \frac{9}{10^k} [/math]
[math] 10x = \lim_{n\rightarrow \infty} \sum_{k=1}^{n} \frac{9\times 10}{10^k} [/math]
[math] 9x = 10x - x [/math]
[math] 9x = \lim_{n\rightarrow \infty} \sum_{k=1}^{n} \frac{9\times 10}{10^k} - \lim_{n\rightarrow \infty} \sum_{k=1}^{n} \frac{9}{10^k} [/math]
[math] 9x = \lim_{n\rightarrow \infty} \sum_{k=1}^{n} \frac{9\times 10}{10^k} - \sum_{k=1}^{n} \frac{9}{10^k} [/math]
[math] 9x = \lim_{n\rightarrow \infty} \sum_{k=1}^{n} \frac{9\times 10}{10^k} - \frac{9}{10^k} [/math]
[math] 9x = \lim_{n\rightarrow \infty} \sum_{k=1}^{n} \frac{9\times 9}{10^k} [/math]
[math] x = \lim_{n\rightarrow \infty} \sum_{k=1}^{n} \frac{9\times 9}{10^k} \times \frac{1}{9} [/math]
[math] x = \lim_{n\rightarrow \infty} \sum_{k=1}^{n} \frac{9}{10^k} [/math]
[math] x = 0.999... [/math]

>>	Anonymous Tue Jan 10 23:25:02 2023 No.15114469 >>15114436 No. 1=1 Even captcha says KYSPJT

Anonymous Wed Jan 11 00:46:22 2023 No.15114660 [DELETED]

>>15112598
>By induction
See >>15114466
>By appeal to intuition
You cannot divide a bottle of water into 3, you can divide the volume of the bottle of water into 3.
From the start a volume can only be expressed in a dimension corresponding to a volume, something like meters cubed, milliliters etc.
You can also divide the mass of the water contained into three smaller bottles so they each weigh the same. Those are two different units defined in two different dimensions.
There is "one bottle" but there is no "1/3" of a bottle. There is "1/3 of the volume of the bottle", "1/3 of the weight of the bottle", "1/3 of the radius of the bottle etc".
In the world of natural numbers 1 divided by 3 equals 0, if you split one bottle into three there is no bottle left.
>By convergence theorem
There is a difference between "converges to" and "equals".
Like I said before there are real numbers between 0.999... and 1.

Anonymous Wed Jan 11 01:02:34 2023 No.15114704

>>15114466
That's utterly inconclusive, but nice triple dubs. This can still show that 0.999...=1
[math]10x=lim_{n\to\infty}\Sigma^{n}_{k=1}\frac{9*10}{10^k}[/math]
[math]10x=lim_{n\to\infty}\Sigma^{n-1}_{k=0}\frac{9}{10^{k-1}}[/math]
[math]10x=9+lim_{n\to\infty}\Sigma^{n-1}_{k=1}\frac{9}{10^k}[/math]
[math]9x=10x-x[/math]
[math]9x=9+lim_{n\to\infty}\Sigma^{n-1}_{k=1}\frac{9}{10^k}-lim_{n\to\infty}\Sigma^{n}_{k=1}\frac{9}{10^k}[/math]
[math]9x=9[/math]
[math]x=1[/math]

Anonymous Wed Jan 11 01:07:04 2023 No.15114714

>>15114704
Actually, to refine it, I should have simplified
[math]9x=9+lim_{n\to\infty}\Sigma^{n-1}_{k=1}\frac{9}{10^k}-lim_{n\to\infty}\Sigma^{n-1}_{k=1}\frac{9}{10^k}[/math]
to
[math]9x=9-lim_{n\to\infty}\frac{9}{10^n}[/math]
or
[math]x=1-lim_{n\to\infty}\frac{1}{10^n}[/math]
Which yields
[math]x=1[/math]

Anonymous Wed Jan 11 01:30:57 2023 No.15114754

>>15111209
Here’s the simplest argument if you actually know basic real analysis.
0.99… is a real number. For any real numbers a and b, if a<b, then there exists real number c such that a<c<b. Suppose 0.99… < 1. Then there must be some real value x such that 0.99… < x < 1. Notice that 0.99… = sum of (9/10^i) as i goes from 1 to infinity.
Since all real values can be defined as an infinite decimal expansion, and x < 1, we can define x by the infinite sequence Sn such that x = sum of Si/10^i as i goes from 1 to infinity. Define 0.99… similarly, using the sequence Tn instead. It is trivial to see that, for all i, Ti = 9. Also note that for all i in [1, infinity), 9 >= Si. But in order for 0.99… > x to hold true, there must exist at least some i in [1, infinity) such that Si > Ti. Obviously none exists, since as stated before, Si <= 9 = Ti for all i in [1, infinity). This is a contradiction, and therefore no such value x exists, and therefore 0.99… = 1.
In simpler terms for brainlets, 1 is not less than 0.99…, and there is no space between 0.99… and 1 for a single real number to exist, so therefore they must be equal.
If you don’t understand why the statement “for all a, b in R, if a<b then there exists c in R such that a<b<c,” then you have not studied enough basic fucking mathematics to discuss the question of 0.99… = 1. Might I recommend baby Rudin, or maybe a basic proofs textbook if the words in baby Rudin are too big for you?

In short, people who say 0.99… =/= 1 after seeing a legitimate proof either don’t know what a real number is, are fucking retarded, or don’t believe in the real numbers/infinite sequences. All 3 of these are good reasons to ignore these people.

>>	Anonymous Wed Jan 11 01:33:11 2023 No.15114759 >>15114754 > But in order for 0.99… > x to hold true Typo. Meant “<”

Anonymous Wed Jan 11 01:35:25 2023 No.15114763 [DELETED]

>>15114754
>In simpler terms for brainlets, 1 is not less than 0.99…, and there is no space between 0.99… and 1 for a single real number to exist, so therefore they must be equal.
They're not equal, but because they approximate each other, under any meaningful level of precision the results of doing mathematical operations with either number will have the same result. You can only discern the difference with infinite precision and that's not useful.

>>	Anonymous Wed Jan 11 01:45:19 2023 No.15114776 >>15111209 1/3 = 0.33333.... multiply both sides by 3 to get 3/3 = 0.9999999... 1 = 0.999999999....

>>	Anonymous Wed Jan 11 02:03:21 2023 No.15114802 >>15114776 >1/3 = 0.33333.... This is not true tho, there is always 1/3 missing

Anonymous Wed Jan 11 02:44:01 2023 No.15114871

[math]
x= \frac{1}{10} \\
0. \overline{9}=9x+9x^2+9x^3+9x^4+ \cdots \\
0. \overline{9}=9x \left (1+x+x^2+x^3+ \cdots \right ) \\
0. \overline{9}=(1-x) \left (1+\mathbf{x}+x^2+\mathbf{x^3}+x^4+ \cdots \right ) \\
0. \overline{9}=1-x+ \mathbf{x-x^2}+x^2-x^3+ \mathbf{x^3-x^4}+x^4-x^5+ \cdots \\
0. \overline{9}=1
[/math]

>>	Anonymous Wed Jan 11 03:40:53 2023 No.15114965 >>15114408 0.00... and then a 1

>>	Anonymous Wed Jan 11 03:49:02 2023 No.15114973 >>15114776 first of all 0.333... is assumed irrational

>>	Anonymous Wed Jan 11 03:50:08 2023 No.15114974 If you allow 1 to be 0.999999 Then then you allow every real number = 0.000....1 less than itself If you add a bunch of them, the error becomes significant Math is a scam wake up, sheeple.

>>	Anonymous Wed Jan 11 04:01:40 2023 No.15114991 https://youtu.be/jMTD1Y3LHcE

>>	Anonymous Wed Jan 11 04:07:29 2023 No.15114997 >>15114973 irrational means no pattern. >0.333333333.......... see a pattern?

Anonymous Wed Jan 11 16:00:05 2023 No.15116018

>>15111209
Fun fact: 0.9999... is not equal to one using the original purpose of the ellipsis (...) symbol (extend series elements infinitely). They literally changed the ellipsis symbol to mean taking the limit for these sorts of numbers because instead of clearing up confusion, math tards would just go ahead and change the definition so not to be wrong.

>>	Anonymous Wed Jan 11 16:22:21 2023 No.15116070 >>15113733 I don't exist tho.

>>	Anonymous Wed Jan 11 16:25:07 2023 No.15116077 >>15113480 It's arithmetic retard, algebra involves variables.

>>	Anonymous Wed Jan 11 16:27:57 2023 No.15116090 File: 266 KB, 1024x1024, 1673385007406.jpg [View same] [iqdb] [saucenao] [google] >>15111279 based retard

Anonymous Wed Jan 11 20:05:16 2023 No.15116563

>>15114776
Saying 1/3 = 0.333... is simplifying the truth, if you do the division algorithm you'll always get a remainder, no matter how much you divide.
That remainder is [math] 0.000... = \lim \frac{1}{10^n} [/math]
So 3 * 1/3 = 3*0.333... + 0.000.. because that is how whole number division works.

>>	Anonymous Wed Jan 11 20:12:05 2023 No.15116580 >>15114974 But 0.0...001 doesn't exist because I can always add another 0

>>	Anonymous Wed Jan 11 20:13:41 2023 No.15116582 File: 19 KB, 665x326, 10400000..png [View same] [iqdb] [saucenao] [google] quints have already decided this

>>	Anonymous Wed Jan 11 20:18:14 2023 No.15116593 Also 0.000... is not zero. [math] \lim 10^n \times 0 = 0 [/math] [math] \lim 10^n \times \lim \frac{1}{10^n} = \lim \frac{10^n}{10^n} = 1 [/math]

Aether king of sci Wed Jan 11 20:23:55 2023 No.15116600
File: 279 KB, 1120x935, 1672142095616034.jpg [View same] [iqdb] [saucenao] [google]

0.999... is a cycling number.
It doesn't equal 1, it almost equals 1 but infinitely so, thus, sometimes it WILL equal 1. There is a 'linking' almost increase event hidden in that symbol.

/Thread

>>	Aether king of sci Wed Jan 11 20:25:40 2023 No.15116602 >>15116600 You're missing 3 numerals in your base 10 retardation otherwise it would make sense. Now if you would please get.. the fuck... Off mah sci

Aether king of sci Wed Jan 11 20:30:38 2023 No.15116611

>>15116593
That's because are you retarded the first 0.0 is the thing that's positively increasing with additional .00 .000 so 0.0000 is moving away from 0. This is proof that the LateX users are just retards hidden behind intolerable nonsensical language/code. Fuck off mah sci now

>>	Aether king of sci Wed Jan 11 20:34:52 2023 No.15116615 STOP THIS NONSENSE ON MAH SCI NOW STOP POSTING STOP TROLLING STOP WHINING, ITS CHILDISH

>>	Anonymous Wed Jan 11 21:12:48 2023 No.15116683 >>15111209 ITT: filtered real-analysis brainlets and midwits who couldn't pass real-analysis class dishonoring Chad ultrafinitists like Wildberger, who could easily pass a real-analysis class if he wanted to.

Anonymous Thu Jan 12 02:05:51 2023 No.15117293
File: 244 KB, 1080x1559, 1600622970116.jpg [View same] [iqdb] [saucenao] [google]

At where is the practical delineation line between 0.999... and 1? At what resolution do the practical limitations of reality make the distinction inconsequential under all possible circumstances?

>>	Anonymous Thu Jan 12 04:25:31 2023 No.15117525 >>15111209 >Creating thread about [math]\frac{3}{3}[/math] over and over, for years Definition of insanity

>>	Anonymous Thu Jan 12 10:00:18 2023 No.15118043 Wonders of mathematicians >We can proof that there is 927n^8-ei dimensions using blurgh, blargh and gnarl. >Cannot see that 1/3 is not 0.333... but only the closest approximation when using decimals and whole numbers

>>	Anonymous Thu Jan 12 10:01:35 2023 No.15118046 >>15118043 how close is this approximation? what is missing?

>>	Anonymous Thu Jan 12 10:07:56 2023 No.15118057 >>15118046 >How close Very close but not exact/precise >Whats missing 1,2,3 4,5,6 7,8,9 0 <- How to group 10 things into thirds

>>	Anonymous Thu Jan 12 10:24:54 2023 No.15118072 File: 71 KB, 976x709, 31252.jpg [View same] [iqdb] [saucenao] [google] >ITT: highschool dropouts cannot fathom a simple definition

>>	Anonymous Thu Jan 12 10:31:10 2023 No.15118082 >>15118057 >Very close Is there some even better approximation?

>>	Anonymous Thu Jan 12 10:38:58 2023 No.15118091 >>15118082 Yes, forexample using different bases. 0.333.., 0.666.., 1 for base 9 0.444.., 0.888.., 1 for base 12

>>	Anonymous Thu Jan 12 10:40:35 2023 No.15118093 >>15118091 made an oopsie.. these threads are just so retarded.. 0.3, 0.6, 1 for Base9 0.4., 0.8, 1 for Base12

>>	Anonymous Thu Jan 12 11:15:00 2023 No.15118132 >>15116563 Since the tree dots denotes etcetera, isn't 0.000... just an infinite string of zeroes? i e zero

Anonymous Thu Jan 12 16:22:08 2023 No.15118582

>>15114066
>Infinity is simply a representation of something never ending.
>never ending
Ah yes, the resort to even more pseudo-scientific nonsense. There is no such thing as an infinity.
>0.999... has no last 9 and no more numbers can be added to it. It's what 0.999... means.
If we were to apply the standards of analysis and set theory and write the extended natural numbers in interval for, [math] [1, \infty] [/math] there is an upper bound called [math] \infty [/math] so there is an [math] \infty[/math]th decimal place which contains a 9. This is the last 9 to the alleged number with an infinite number of 9's "0.999..." = 0.999... 9. So 10* 0.999 = 10* (0.999...9) = 9.999...0.
>>15114124
There is no such thing a "real" number. There is no such thing as a "set" as you have not defined it and no mathematician has ever defined it.

Anonymous Thu Jan 12 16:33:06 2023 No.15118602
File: 194 KB, 1284x1233, 210AB981-8145-4B64-A0C1-C5AEF9DECA1F.jpg [View same] [iqdb] [saucenao] [google]

>>15111209
Technically, don’t we have multiple infinities as we approach zero in all directions? Couldn’t this just be the beginning of infinity? Last time I checked, one is not infinity. Doesn’t this make you all morons for not thinking that?

>>	Anonymous Thu Jan 12 16:45:22 2023 No.15118627 >>15118602 No. There are no infinities. Your graph ends at explicit points.

>>	Anonymous Thu Jan 12 16:46:22 2023 No.15118629 >>15118582 The interval can't be closed [1, infinity] doesn't make sense Has to be [1, infinity [ Since there is no upper bound

>>	Anonymous Thu Jan 12 16:47:24 2023 No.15118633 >>15118582 Alright simpler words then. How many numbers are there?

>>	Anonymous Thu Jan 12 16:51:21 2023 No.15118639 >>15118627 I guess you’re a literal retard that can’t conceptualize simple ideas. It projects infinite both ways.

>>	Anonymous Thu Jan 12 16:51:46 2023 No.15118641 >>15118629 Not according to modern set theory and analysis. It can be closed and it is closed. >>15118633 There are only as many numbers as those which has been explicitly written down.

>>	Anonymous Thu Jan 12 16:52:08 2023 No.15118644 >>15118629 Brainlet who doesn't know what compactification is.

Anonymous Thu Jan 12 16:56:27 2023 No.15118646

>>15118639
>can’t conceptualize simple ideas
Rather that's you as you're taking a simple idea from geometry, that something simple like a curve or line segment can be extended, and then in your lack of understanding that it's simply as its stated, need to imagine there must now be objects out the exist out of nowhere called "infinities" when this doesn't even logically follow.

Anonymous Thu Jan 12 17:03:29 2023 No.15118656

>>15118641
For any such number that has been written down I can write down a bigger one.
How many numbers are there?

Per definition, infinity is unbounded. The only characteristic of it is that it is not finite. Making it finite makes it ininfinite.

Are you sure that compactification is useable here in this context? That we'll still get the same results?

Like I get that you just hate the whole concept of infinity and think it shouldn't exist. But excluding it really causes you to beat around the bush or to redefine it. Which is weird.

Anonymous Thu Jan 12 17:07:10 2023 No.15118662

>>15118646
> [-infty,+infty]
> affinely extended real number system
I was pointing out a possible scenario where 0.9999999 isn’t one. Seethe more.
https://en.m.wikipedia.org/wiki/Extended_real_number_line
https://mathworld.wolfram.com/AffinelyExtendedRealNumbers.html

>>	Anonymous Thu Jan 12 17:11:31 2023 No.15118673 >>15118662 >"The normal nonsense isn't good enough so I have to make up more nonsense" You really are a retard.

>>	Anonymous Thu Jan 12 17:14:09 2023 No.15118679 >>15118673 Thanks! I’m trying

Anonymous Thu Jan 12 17:23:35 2023 No.15118691

>>15118656
>For any such number that has been written down I can write down a bigger one.
Then write it down and I'll say that number exists. Until you write it down it's nothing but talk and therefore meaningless.
>How many numbers are there?
Only the amount of numbers that have been explicitly written down.
>Per definition, infinity is unbounded.
There is no such thing as an infinite
>The only characteristic of it is that it is not finite
Define finite. The only possible definition is something like you can assign a natural number to it in an appropriate fashion like the number of marbles in a box. In this case infinite (which is not the same thing as this fictional "infinity") is just the logical negation of finite. That means exactly that you cannot assign a natural number. This does not justify the assumption that an object (or whatever nonsense is posited) called "infinity" exists.
>Are you sure that compactification is useable here in this context?
According to the axiom of choice, it is usable here in this context.
>That we'll still get the same results?
We get the result that 1-.999... = 1.000...00-.999...99 = 0.00...01 by the axiom of choice.
>Like I get that you just hate the whole concept of infinity and think it shouldn't exist.
The reality is that there is no such thing as an infinity in these contexts.
>But excluding it really causes you to beat around the bush or to redefine it
Incorrect. Whatever the term "infinity" refers to is undefined it is not justified in these contexts and it still isn't. Whereas "infinite" ([math] \not= [/math] infinity) is just the logical negation of finite. Finite itself needs to be defined rigorously such as in the case where finite means you can count some number of objects like the number of marbles in a box.

Anonymous Thu Jan 12 17:28:05 2023 No.15118697

>>15118691
> Whatever the term "infinity" refers to is undefined
Isn’t this statement your opinion and not universally agree to it, I.g. Cope?

> However, the expressions +infty+(-infty), -infty+(+infty), and 0/0 are undefined. The above statements which define results of arithmetic operations on R^_ may be considered as abbreviations of statements about determinate limit forms. For example, -(+infty)=-infty may be considered as an abbreviation for "If x increases without bound, then -x decreases without bound." Most descriptions of R^_ also make a statement concerning the products of the improper elements and 0, but there is no consensus as to what that statement should be. Some authors (e.g., Kolmogorov 1995, p. 193) state that, like +infty+(-infty) and -infty+(+infty), 0·(+/-infty) and +/-infty·0 should be undefined, presumably because of the indeterminate status of the corresponding limit forms. Other authors (such as McShane 1983, p. 2) accept 0·(+/-infty)=+/-infty·0=0, at least as a convention which is useful in certain contexts.

>>	Anonymous Thu Jan 12 17:30:05 2023 No.15118699 >>15118691 Then you admit you have no clue how many numbers exist. If we don't know how many nimbers exist, how can we prove something is true for all numbers?

>>	Anonymous Thu Jan 12 17:31:11 2023 No.15118701 >>15118691 All I'm asking of you is to tell me how many nines 0.999... has

>>	Anonymous Thu Jan 12 17:33:38 2023 No.15118706 >>15118691 It seems to me like you've gone and cherrypicked a couple of axioms and definitions you believe in. Completely disregarding the current case. Name what writing 0.999... means.

>>	Anonymous Thu Jan 12 17:38:45 2023 No.15118713 >>15118701 The 0.99999 increase without bounds, how’s that?

Anonymous Thu Jan 12 17:48:04 2023 No.15118726

>>15118697
>Isn’t this statement your opinion and not universally agree to it
Not an opinion. It's a fact. It does not exist. Moreover, assuming such a thing exists leads to a variety of paradoxes like the Russel paradox.
>>15118699
>Then you admit you have no clue how many numbers exist.
In the context where one can introduce one more number into a list from an algorithm, then there is no such thing as the "number of numbers."
>If we don't know how many nimbers exist, how can we prove something is true for all numbers?
You don't need to know anything about how many numbers exist or anything along those lines to prove something is true. It's simply using a generic placeholder to do a form of algebra or logic. The number of objects of a certain type is never needed.
>>15118701
There are three 9's.
>>15118706
>It seems to me like you've gone and cherrypicked a couple of axioms and definitions you believe in
I don't believe in those axioms. But since they are believed in by contemporary mathematicians, I'm going to use them. The Axiom of Choice does infer that a decimal supposedly consisting only of an infinite number of nines to the right of the decimal place in fact has a final 9.
>Name what writing 0.999... means.
In terms of what it actually means, you wrote 0, a period, then three nines. After which "..." is just a placeholder for all sorts of fancy. In fact, without further specification, it means either nothing or that I can simply add on whatever digit I please after the first three 9's.

>>	Anonymous Thu Jan 12 17:56:47 2023 No.15118734 >>15118726 > Russell Paradox Interesting thank you

>>	Anonymous Thu Jan 12 19:11:39 2023 No.15118919 >>15111209 you're correct 0.999... is not a number and thus not 1

>>	Anonymous Thu Jan 12 22:54:06 2023 No.15119387 >>15111209 I will say, it can never be 1 and thats just how it is.

>>	Anonymous Fri Jan 13 00:11:37 2023 No.15119561 literally what is the point of calculating involving anything less than the planck constant. useless metaphysics shit

>>	Anonymous Fri Jan 13 08:31:02 2023 No.15120402 >>15111209 If two numbers are unequal, then there must be a number between them. There are clearly no numbers between 0.999... and 1. Therefore, 0.999... and 1 must be two representations of the same number. Case closed.

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/sci/ - Science & Math