The original poster presents a problem comparing the values of cos(sin(x)) and sin(cos(x)), seeking to determine which is greater through proof. The context involves concepts from trigonometry and function composition.
The discussion is ongoing, with participants providing feedback on the original poster's approach and raising concerns about the logical structure of the proof. There is no explicit consensus on the correctness of the proof or the methods being employed.
Some participants highlight potential omissions in the original poster's statements and question the appropriateness of using proof by contradiction for the problem at hand. The nature of the problem and the assumptions being made are under scrutiny.
Mark44 said:Something you asserted early on is not true - that f(g(x)) = g(f(x)). I stopped reading after that.
You would have been doing a proof by contradiction if you said you were doing a proof by contradiction. The way you've written it, you're just asserting (without justification) something that is not even true.Sylvester Sly said:I was doing proof by contradiction. In order to prove f(g(x)) =/= g(f(x)) i started off by letting f(g(x)) = g(f(x)) and working from there.
I assumed that was a typos for "g(f(x))= f(g(x))= cos(sin(x))". But, in any case, if the problem was to determine which was larger, I don't see what a proof by contradiction that they are not equal would accomplish.Mark44 said:If you're doing a proof by contradiction, you don't start with "therefore ..." - You start by assuming the thing you want to contradict.
Also, in the same line you have "Therefore g(f(x)) = f(g(x)) cos(sin(x))". It looks like you omitted part of what you wanted to say.