Fix typo in Chapter 1 Exercise 2.2 proof of Proposition 2.1

[Copilot]

Summary

Fixes a typo in the proof of Proposition 2.1 (part 2) in Chapter 1, Exercise 2.2, as reported in issue #[number].

The Problem

In the proof's construction of the right-inverse function g:B→A, line 203 incorrectly stated:

We want to construct a function g:B→A such that f(g(a)) = a for all a∈A.

This is mathematically incorrect because:

• The function g has domain B (not A), so g(a) where a∈A doesn't make sense
• The goal is to prove g is a right-inverse of f, meaning f∘g = id_B, which requires f(g(b)) = b for all b∈B

The Fix

Changed line 203 to correctly state:

We want to construct a function g:B→A such that f(g(b)) = b for all b∈B.

This makes the proof logically consistent with:

• Line 199: which correctly shows f(g(b)) = b in the forward direction
• Line 217: which correctly concludes f(g(b)) = b as the result

The rest of the proof remains unchanged and correct.

Original prompt

---

This section details on the original issue you should resolve

<issue_title>1.2.2 typo</issue_title>
<issue_description>Hello, in the proof of Proposition 2.2 in chapter 1 (Exercise 2.2), you claim $$f(g(a))=a$$, not $$f(g(b))=b$$. The rest of the proof is correct,</issue_description>

<agent_instructions>Fix Chapter 1 Exercise 2.2. </agent_instructions>

Comments on the Issue (you are @copilot in this section)

Fixes #17

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