/sci/ - Science & Math

>>15226901
dense ordering of reals would become fuddlore, which it already should

>>15165480
Writing down a symbol as shorthand for a type of object is not the same as collecting objects of that type.

>>15158805
That has never been done.
>Dedekind cuts: just sophistry, no real numbers ever derived from this method--relies on the supposition that real numbers exist to even discuss potential examples in which case this relies on circular reasoning
>cauchy sequences: let's just define the thing we claim converges to a real number to be that real number--circular reasoning
>intervals: just a souped up version of the cauchy sequence version in interval form--also relies on circular reasoning
>infinite lines in the Stern-Brocot tree: the law of logical honesty states that you cannot claim you can do things you actually can't.

>>15156279
You started by assuming there was such a thing as the real numbers when no one ever in history has provided a definition of such a number. Any alleged attempts have always been some strange constructions that have severe logical problems such as circular reasoning or assuming that one can do an infinite number of things when they can't.

>>15142168
>neighborhood of infinity
>"real" number

>>15119091
Real numbers and ZFC are modern religious fantasies.

>>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.

>>15103017
>an infinite of infinites
Utter nonsense

Ah yes. Quite a bit of damage. Foundational concerns are incredibly important to mathematicians even if the average modern mathematician wants to ignore it.

>Everything is a set of a set of a set

>>15044067
Then potentially the smallest gold "bar" is exactly one gold atom. The smallest a chest can be therefore is just large enough to exactly fit one gold atom. That is assuming that a chest that size can even exist in the first place. Apply the previous criticism and this remains an ill-conceived illogical problem.

Your argument defeated itself in the first few lines.
>Using ZFC
>Using the axiom choice
>Set of all that "exists"
>Special definition of exists that includes absolutely every idea, fantasy, myth, etc. It even contains God
>Reference to cardinalities
>unspecified order relation
>asserted consequence is that God is conceived of by the human mind (special definition of exists); something that the argument is premised upon
Why don't you just use the Kalam Cosmological argument?

The "reals" just aren't real.

You can't even realistically expect to solve the vast majority of polynomials with rational coefficients you could write down. Why you start to involve power series into the thing you really get to the point where you absolutely can't do anything as solving the equations would involve an infinite number of steps given that the exponential function is supposed to be a power series that can't even be evaluated in total by human beings.

Simply put, there is no solution.

>>14963935
I'm sure you can assert there's an algebra of fairies and unicorns too. It doesn't make these things any better defined.