How do I refute or prove this?

  • Context: Undergrad 
  • Thread starter Thread starter Monsu
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Discussion Overview

The discussion revolves around the composition of functions, specifically the expression f o g = (lambda)x.x, and the implications regarding the existence of an inverse function. Participants explore the definitions and interpretations of the functions involved, as well as the notation used.

Discussion Character

  • Debate/contested, Conceptual clarification

Main Points Raised

  • One participant questions the understanding of the problem, stating that if f has an inverse, it should be f^-1: B->A, and not the function g as defined.
  • Another participant asserts that f o g is not a function and emphasizes the standard reading direction for function composition, suggesting confusion in the original question.
  • Concerns are raised about the notation used, including the meaning of "lambda," the significance of the dot between the xs, and the overall clarity of the input in the composition.
  • A participant expresses feeling overwhelmed and thanks others for their input, indicating a struggle with the complexity of the topic.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus, as there are differing interpretations of the problem and the notation involved. Confusion remains regarding the definitions and roles of the functions in question.

Contextual Notes

There are unresolved questions about the notation and the assumptions underlying the definitions of the functions and their compositions. The discussion highlights potential misunderstandings about function composition and inverses.

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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