Question 1179552: Prove that if f : A → B is a function from A to B, then f ◦ iA = f and iB ◦ f = f.
(iA: inverse of A).
Answer by ikleyn(52779)   (Show Source):
You can put this solution on YOUR website! .
Prove that if f : A → B is a function from A to B, then f ◦ iA = f and iB ◦ f = f.
(iA: inverse of A).
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Then (f o iA) is identical map of the image of A (which is part of B) to B.
It is NOT TRUE that (f o iA) = f, as you write in your post.
Also, then (iA o f) is identical map of A to A.
It is NOT TRUE that (iB o f) = f, as you write in your post.
Also, notice that " iB " is not defined in this problem and in this post, at all.
" iB " is totally fictitious subject, irrelevant to this problem.
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Where, from which source, did you retrieve these incorrect statements ?
Do you create / compose / invent them on your own ?
If you retrieve it from some source, then keep in mind that this source is UNTRUSTED.
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Notice that in this my post, I make not only my work as a tutor.
I make your part of work, too (also), trying to formulate the problem CORRECTLY.
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And the final note.
Everything what I wrote above, is written under the assumption that iA is the inverse of A, as it is stated in your post.
I think that it is the key error in your post.
If to assume that iA is IDENTICAL map of A to itself,
and if to assume that iB is IDENTICAL map of B to itself,
then all statements in your post become a) correct and b) self-evident.
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