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>that guy whose solution to literally every proof is induction

>>10106888Bump

>>10106888That's not that bad at all, and it's pretty rare. Those guys are nothing compared to the>every single proof is by contradictionfuckers, who are everywhere. I've even had professors who write like this. Drives me batshit.

>>10106946Those are the best proofs.

>>10106946The chad nonconstructive proof vs the virgin proof by construction.

>>10106888wow their faces

>>10106946>"assume X with said properties does not exist">proceeds to find X>"we have arrived at a contradiction, therefore our theorem holds"

>>10106946>that guy who phrase induction proofs as proofs by contradiction

>>10106888I often get the feeling the Bog nay-sayed my theory.

>>10106946contradiction is the most powerful tool you fucking faggot

>>10107133jon, what did you use to make those figures in the top left (the lightcones-on-trajectories and the 3D rectangle sheets)? TikZ?

>>10106992I 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

>>10107204>2 linesYou mean n congruent to 0 implies n^2 congruent to zero, etc?

>>10107210no

Onions

>>10107335Which one, then?

>>10107353??? 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

>>10107360that's because 0^2 and 2^2 is congruent to 0 mod4 and 1^2 and 3^2 is congruent to 1 mod4

>>10107378??? This is something which I already know

>>10107382just pointing it out for no reason

>take base case as definition>inductive step, assume true for n-1> define quantity at n>QED

>>10106992Honestly I don't even like the usual proof that there are infinitely many primes. Just rephrase it without contradiction:Take any finite set of primesTheir product +1 is not divisible by any of themTherefore no finite set of primes is completeTherefore infinite primesNo reason to say "Assume finitely many primes."

>>10106888In 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

>>10107517This is also why I hate the typical diagonalization argument.