Mathematical induction doesn't make any sense
>>17046886The naming doesn't make sense. It's just recursive deduction.
>>17046886why>>17046889why
>>17046965Because
>>17046966because what
>>17046971Yeah
>>17046980what
>>17046990Exactly
OPs post is terribleEvery reply to a terrible post is terribleTherefore this thread will necessarily be terrible
>>17047004What?
>>17047004heh, it do be like dat
Not much difference than magnetic induction
>>17046886No it's actually a very logical proof method.
>>17047175why
>>17047175>it's true for 0>it's true for 1>so it's true for every numberlogical fallacy
>>17047260>prove that if some condition holds for an arbitrary element in the sequence, it holds for the next one as well>prove that the condition holds for the first element in the sequenceYou've thus proven that it holds for every element. What's the problem, brainlette?
>>17047272Just because the condition holds for 0 and the next number doesn't mean it holds for every number.
>>17047335Just because you're a profound retard who can't read doesn't mean you get to enjoy ignorant bliss. I will make it unpleasant for you to post your mongoloid opinions.
>>17047004but that was a good point...
>>17047335Reading comprehension. He explicitly stated that you must first prove: >if some condition holds for an arbitrary element in the sequence, it holds for the next one as wellIf you can prove that:>if it holds for n, then it also holds for n+1And also:>it does, indeed, hold for nThen you can prove it holds for all elements in the sequence by simply making n+1 your new n. But these kinds of proofs necessarily require that it doesn't matter what n is so long as it is present in the sequence in question.
>>17047260thats not induction
>>17047272What if there’s some nonstandard part of the numbers you can get to from 0, off the side somewhere
>>17047614Always specify for which set your proof applies. Not all things are going to be true for the complex numbers which are true for the reals.
>>17047614I don't see anything in my post about numbers, standard or otherwise. Retarded cattle.
assumptions assumptions assumptions. it's all about the ass. it is an art, few are capable to properly wield it
>>17046992whathow about u verify ur a human u dumb nigleet
>>17047004A thread is much more than the sum of its component parts, Anon.A thread is emergent. Much more so on /sci/.
>>17047716No
>>17048037yes
>>17048042Why?
>>17047723The average /sci/ thread may as well emerge from is a dog's anus without loss of meaning or value.
>>17047335>doesn't mean it holds for every number>an arbitrary element
>>17048049>assume the property holds for every arbitrary number>then the property holds for all numbers
>>17048097holy shit you people are really barely making the double digit IQ threshold.>prove that "IF the claim is true for some statement in an infinite sequence, THEN it is also true for the next entry">prove that the claim is true for the first in the sequenceIt's really not a difficult concept. And it can always be spelled out for room temp in Celsius IQs like you by repeating the proven IF...THEN as many times as it takes manually.
>>17047004I present ro you Anon's last theorem.
>>17048109>"IF the claim is true for some statement in an infinite sequence, THEN it is also true for the next entry"but isn't that what we're trying to prove in the first place?
>>17048124Almost but not quite, that is the brilliance of induction.As long as you can order the claims you make according to an index, like c(1), c(2), ... , being able to prove "if c(n) is true, then c(n+1) is true" means you no longer have to prove infinitely many individual c(n) but can prove them successively because you formalized how to ad infinitum. Suppose you prove c(2). Then you can use the lemma "if c(n) then c(n+1)" to prove c(3), and re-apply that as often as you like.However, it would say nothing about c(1), which you would still have to prove.
>>17048144damn u replied too much. now nobodys responding, no more idiots to entertain me. thats on u
>>17048179niglet
>>17048182nugget
>>17048144>if c(n) is true, then c(n+1) is truebut doesn't that follow trivially from c(n) being true for EVERY n? because then it would be true for n+1 automatically
>>17048190I'll play:Let's say you wanted to prove all even numbers are divisible by 2 and you insisted on induction to do this (retarded and inefficient, but whatever). Here's how that plays out:>define your set as 2n>if it so happens that 2n is divisible by 2, show that 2(n+1) is also divisible by 2>2(n+1) = 2n+2>You're just adding another 2 to the number we already assumed divisible by 2, so that number is trivially also divisible by 2>now show it is true for n=1>2(1) = 2>2/2 = 1, so it's divisible by 2>since 2(n) is divisible by 2 for n=1, we know it is also true for n=2, which proves it's true for n=3 and do on...>2(n) is divisible by 2 for all n >= 1QED
>but doesn't that follow trivially from c eating breakfast EVERY day? because then it would be true for tomorrow automatically>brainlet.webmImagine coming to /sci/ - Science & Math just to get filtered repeatedly by Science & Math in public.
>>17048194But 2(n+1) is already divisible by 2. Seems like overkill
>>17048199Now imagine it was something less obvious and it didn't have breakfast this morning.
