/sci/ - Science & Math

[Anonymous No.9775646]

>proof by induction

[Anonymous No.9775650]

>argument by frogposting

[Anonymous No.9775659]

>>9775650
based

[Anonymous No.9775688]

>>9775646
I unironically still don't understand why induction actually works. Looks like pulling yourself up by your bootstraps to me. t. Bachelor Math

[Anonymous No.9775752]

>>9775688
more like
>t. american
you prove that the first case is true. Then you prove that if the nth case is true, then you can show that the n+1th case is true. So you showed that the first case is true, therefore the 2nd case is true, therefore the third case is true, etc

[Anonymous No.9775753]

>>9775688
Prove it works for some number n_0
Prove that if it works for for any number n then it also works for n+1.
Thus since it works for n_0, it follows that it also works for n_0 + 1.
Thus it also works works for n_0 + 1 +1 = n_0 + 2
Repeat ad infinitum

[Anonymous No.9775901]

>>9775688
Socrates invented induction. It was recognized by him and every subsequent philosopher that it's synthetic knowledge based on assumption and is therefore not a real proof, although math fags will deny this. It's logically equilvent to claiming "I've ever seen anything move faster than the speed of light" is a sufficient proof for it being the universal speed limit. Induction belongs in the trash like syllogisms and the rest of antiquated logic.

[Anonymous No.9775906]

>>9775646
is there something less retarded? Maybe strong induction? is there a rigorous form of induction?

[Anonymous No.9775909]

>>9775901
mathematical induction and philosophical induction are unrelated except by name

[Anonymous No.9775915]

>proof by contradiction

[Anonymous No.9775930]

>>9775753
human 1=0
human 2=0
human n=0
n-->n+1
human n+1=0
thus if one human is retarded, every human is retarded q.e.d.

[Anonymous No.9775934]

>>9775909
Except they're both based on logic and are essentially the same thing. You observe a particular case and apply it to the universal case, based on an assumption.

[Anonymous No.9775942]

>>9775934
that's philosophical induction, in mathematical induction you PROVE that you get a general rule for successive cases

[Anonymous No.9775950]

>>9775942
You're not proving anything, mathematical induction is synthetic a posteriori and isn't a real proof. It's based on an assumption.

[Anonymous No.9775953]

>>9775950
>I don't know what it means to prove an implication

[Anonymous No.9775957]

>>9775950
but it just werkz every time so I'm sure someone has rigourized it

[Anonymous No.9775958]

>>9775950
its not.
You show that a relation is true for n.
Then you show via a mathematical proof that if it is true for ANY n, it must be true for n+1.
If it is true for n, and it is also true for n plus one, then it must be true for every n since we can say m=n+1 and m goes to m+1, which we showed that the next natural number is true. this it is true for every n q.e.d.

[Anonymous No.9775962]

>>9775950
yes it's based on an assumption, and you prove that it's true for that assumption. you aren't interested in the cases where the assumption is false. so you prove if this is true and it implies a true statement it is true, you don't care about what false statements implie

[Anonymous No.9775963]

please explain how mathematical induction is correct without numbers.

[Anonymous No.9775965]

>>9775963
already done
see
>>9775752
>>9775753
>>9775958

[Anonymous No.9775996]

>>9775950
Mathematical induction is completely deductive, you brainlet.

[Anonymous No.9776027]

>>9775906
>proof by exhaustion

[Anonymous No.9776060]

>>9775934
>"proof" by induction
>based on logic