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#math
<hefty> that way you dont have a bunch of discombobulation
<jerware> if i were to proove: if x^2 is odd, x is odd. so would proof by contradiction be: if x^2 is even, x is even. correct?
<jerware> there
<zbrown> jerware: that'd be proof by contraposition
<TRWBW> jerware: proof by contradiction means proving that any counterexample leads to an impossibility, such as 0=1 or true=false or there is a right triangle where a^2+b^2!=c^2, etc.
<tjcoder> zbrown no... contraposition switches both.
<zbrown> tjcoder: didn't he switch both in this case?
<zbrown> he went from both being odd, to both being even
<tjcoder> zbrown if x is even, then x^2 is even.
<zbrown> oh ok
<zbrown> reverse format
<TRWBW> contropositive switches and negates both the assumption and the consequence.
<zbrown> tjcoder: my mistake then
<tjcoder> zbrown no prob, it happens :-)
<jerware> TRWBW, so if the counter example is impossible, or false, the original statement im an trying to solve is true ?
<TRWBW> contropositive example: the statement x even implies x^2 even is equivalent to x^2 not even implies x not even
<tjcoder> zbrown mostly making sure that *i* wasn't that tired... haha
<zbrown> hah
<TRWBW> jerware: go with god
<jerware> go with god?
<jerware> but i dont belive in god. since my car ended up in a u-pull-it.
<Dacicus> TRWBW: Do spherical right triangles satisfy a^2 + b^2 = c^2?
<andrew_> hey all, trying to prove this. and hitting a pretty big block...: prove by induction, for n >= 3, 3^n + 4^n < 5^2
<andrew_> arg
<andrew_> for n >= 3, n^n + 4^n < 5^n
<TRWBW> Dacicus: nope. they don't satisfy sum of interior angles is pi either. but they have their own formula, basically the difference between the sum of the interior angles and pi depends on the area of the triangle
<andrew_> i get so far as 3^(k+1) + 4^(k+1) < 5^(k+1) and im stuck
<TRWBW> Dacicus: in general the difference of the sum of the angles in a triangle made out of 3 geodesics on a manifold relates to the integral of the gaussian curvature inside the triangle
<Dacicus> Maybe if you write 5^(k + 1) = 5 * 5^k and go from there?
<andrew_> hmm. ill give that a shot (thanks)
<Dacicus> TRWBW: Okay, I didn't understand a significant number of those words you used.
<Dacicus> guess I'll stop now
<andrew_> Dacicus õ hrm. im not sure what to do with that now
<andrew_> ah, damn script
<andrew_> i did alright on the proofs without the k in the exponent
<andrew_> this one is throwing me a major loop. can you help me along any further?
<jerware> so what is a counter example
<jerware> is it an oposite of the original?
<andrew_> jerware ? are you talking to me?
<jerware> anyone
<tjcoder> jerware a counter example works to disprove the statement by finding something that makes it incorrect
<JIMJONESBALLIN> A counterexample is any example that shows the statement to be false.
<Dacicus> andrew_: 5 * 5^k > 5 * (3^k + 4^k) = 5 * 3^k + 5 * 4^k > 3 * 3^k + 4 * 4^k
<jerware> ok
<andrew_> jerware : like saying for all integers n < n^2
<andrew_> jerware : a counter example is n = 1
<parfox> _llll_: You still around?
<andrew_> is it considered bad form to pm people in this channel?
<Dacicus> andrew_: I think most people prefer if you ask first
<TRWBW> Dacicus: it's a neat subject. if you get the chance, take a one semester course in differential geometry. it covers all that classical stuff about triangles on spheres and such and more.
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