How do I refute or prove this?

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The discussion centers on the confusion surrounding the composition of functions, specifically regarding the notation f o g = (lambda)x.x and its implications for inverses. Participants express uncertainty about the definitions of lambda calculus elements, such as the meaning of x and the dot notation. There is a consensus that f o g is not a valid function under standard composition rules, which read from right to left. Additionally, the concept of an inverse function is clarified, emphasizing that if f has an inverse, it should be denoted as f^-1: B->A, not as g. Overall, the conversation highlights the complexities and misunderstandings in function composition and notation in mathematical contexts.
Monsu
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How do I refute or prove this?!

If f o g = (lambda)x.x, then f^-1 = g

given that f:A -> B and g:B -> C
 
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i don't think i understand the problem. if f has an inverse, it would be f^-1: B->A; it wouldn't be that function g as defined.
 
once more, fog is not a function, monsu, the standard is to read from right to left when composing functions. and the first part of your question makes no sense to me. Pretend you don't know what the question is and read it as if for the first time.

what is lambda, why is it in brackets, what is x, what is the dot between the xs? are you multiplying things? what's the input in fog (which isn't even a function?) is it a lambda or an x, or an x.x?
 
You are right Matt, it isn't even a function... my brain seams to be damaging with work overload! Thank you so much, once again!
 
Thanks to you too fourier!
 

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