Discussion about math, puzzles, games and fun. Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ ¹ ² ³ °
 

You are not logged in. #1 20051231 12:40:16
obsessed with proofsI few weeks ago I learned about the critical number (closed interval) theorem. It stated that if f(x) is a function continious on an interval [a,b] the maximum and minimum values on the interval are either at f(a), f(x) or the critical numbers of the function f. I would not have realized this, but its quite obvious once its presented to you. But my mathbook said "the proof of this concept is beyond the scope of this book". Last edited by mikau (20051231 12:45:59) A logarithm is just a misspelled algorithm. #2 20051231 15:37:03
Re: obsessed with proofsI'm not a stickler for proofs, but I believe it's to avoid basing any work on unfounded assertions, obvious though they may seem. El que pega primero pega dos veces. #3 20051231 15:42:17
Re: obsessed with proofsperhaps. But can you prove 2 + 2 will always equal 4? We obvserve it happens every time we try but technically can't prove it. Does that make it less true? A logarithm is just a misspelled algorithm. #4 20051231 17:48:50
Re: obsessed with proofsProofs use the rules and definitions of math. I don't think you can prove the rules; you must define them before you can prove things (chicken and egg, sort of thing). Right? El que pega primero pega dos veces. #5 20051231 17:59:49
Re: obsessed with proofslol! Couldn't resist huh? Don't make me pull out that y = x formula to prove 1 = 2 :P A logarithm is just a misspelled algorithm. #6 20060101 00:18:48
Re: obsessed with proofsThe things that cannot be proved are the axioms. IPBLE: Increasing Performance By Lowering Expectations. #7 20060111 01:40:03
Re: obsessed with proofsHey Mikau...if it's true, then we should be able to prove it, right? You sound surprised that we need to be that rigorous...There are many theorems that seems to be entirely common sense, but we still need to prove them...that is the essence of mathematics...observation, conjecture, and proof...That is the whole point of axiomatic proof...we can only build on what we know when we are certain that we know it... The greatest challenge to any thinker is stating the problem in a way that will allow a solution. Bertrand Russell 