Quote:
Originally Posted by GGG
I don’t like this problem isn’t there a wide variety of sets of numbers that prove the general case of there is at least one irrational number that satisfies the solution and then the debate is just proving the initials conditions are irrational?
Going from memory the construct is something like root 3^ log 4 = 2 and then you prove the construct isn’t true. Anyway I dislike mathematical proofs….
|
I probably should have specified algebraic numbers in the original wording. When we got this problem as an assignment in uni, it didn't specify algebraic numbers, but it did say "consider sqrt(2)" as a hint, which led us down the right path for the solution.
If you consider logs, then the issue is, as you say, proving that the log of some value is irrational, which isn't trivial.
I do think math proofs have a certain beauty about them because they can show an assertion is always true and it is airtight. Also, they often reveal something new about the nature of the system you are working in. Brute force proofs are like the ugly stepchild - they prove the result by just checking every possible scenario, and usually don't reveal anything new - just the result (I know the 4-color problem was initially solved this way. Haven't checked if there is a non-brute force proof for that problem).