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10106888 No.10106888 [Reply] [Original] [archived.moe]

>that guy whose solution to literally every proof is induction

>> No.10106942


>> No.10106946

That's not that bad at all, and it's pretty rare. Those guys are nothing compared to the
>every single proof is by contradiction
fuckers, who are everywhere. I've even had professors who write like this. Drives me batshit.

>> No.10106957

Those are the best proofs.

>> No.10106969
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The chad nonconstructive proof vs the virgin proof by construction.

>> No.10106970

wow their faces

>> No.10106992

>"assume X with said properties does not exist"
>proceeds to find X
>"we have arrived at a contradiction, therefore our theorem holds"

>> No.10107126
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>that guy who phrase induction proofs as proofs by contradiction

>> No.10107133
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I often get the feeling the Bog nay-sayed my theory.

>> No.10107146

contradiction is the most powerful tool you fucking faggot

>> No.10107189

jon, what did you use to make those figures in the top left (the lightcones-on-trajectories and the 3D rectangle sheets)? TikZ?

>> No.10107204

I once tried to prove n^2 is congruent to 0 or 1 mod 4 using induction and contradiction, then I realized i was retarded and wrote the 2 line proof

>> No.10107210

>2 lines
You mean n congruent to 0 implies n^2 congruent to zero, etc?

>> No.10107335


>> No.10107348


>> No.10107353

Which one, then?

>> No.10107360

??? Every natural number is either an even number or an even number plus one, so their square must be congruent to either 1 or 0 mod 4

>> No.10107378

that's because 0^2 and 2^2 is congruent to 0 mod4 and 1^2 and 3^2 is congruent to 1 mod4

>> No.10107382

??? This is something which I already know

>> No.10107385
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just pointing it out for no reason

>> No.10107499
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>take base case as definition
>inductive step, assume true for n-1
> define quantity at n

>> No.10107517

Honestly I don't even like the usual proof that there are infinitely many primes. Just rephrase it without contradiction:
Take any finite set of primes
Their product +1 is not divisible by any of them
Therefore no finite set of primes is complete
Therefore infinite primes

No reason to say "Assume finitely many primes."

>> No.10107582

In some areas, like computability, induction is your standard tool. I've typeset assignments that are over 20 pages long just because they're full of long ass inductions and nested inductions

>> No.10107743

This is also why I hate the typical diagonalization argument.

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