It looks like you're new here. If you want to get involved, click one of these buttons!

- All Categories 2.4K
- Chat 505
- Study Groups 21
- Petri Nets 9
- Epidemiology 4
- Leaf Modeling 2
- Review Sections 9
- MIT 2020: Programming with Categories 51
- MIT 2020: Lectures 20
- MIT 2020: Exercises 25
- Baez ACT 2019: Online Course 339
- Baez ACT 2019: Lectures 79
- Baez ACT 2019: Exercises 149
- Baez ACT 2019: Chat 50
- UCR ACT Seminar 4
- General 75
- Azimuth Code Project 111
- Statistical methods 4
- Drafts 10
- Math Syntax Demos 15
- Wiki - Latest Changes 3
- Strategy 113
- Azimuth Project 1.1K
- - Spam 1
- News and Information 148
- Azimuth Blog 149
- - Conventions and Policies 21
- - Questions 43
- Azimuth Wiki 719

Options

What is the inverse \( f^{−1} : 3 \rightarrow A \) of the function \(f\) given below?

How many distinct isomorphisms are there \( A \rightarrow 3 \)?

The set \( A := \{a, b, c \} \) and the set \( \underline{3} = \{1, 2, 3 \} \) are isomorphic; that is, there exists an isomorphism \( f : A \rightarrow \underline{3} \) given by \( f(a) = 2, f(b) = 1, f(c) = 3 \).

## Comments

\(f^{-1}(2)=a,f^{-1}(1)=b,f^{-1}(3)=c\)

There is one for each permutation on three elements, so there are 3!=6.

`1. \\(f^{-1}(2)=a,f^{-1}(1)=b,f^{-1}(3)=c\\) 2. There is one for each permutation on three elements, so there are 3!=6.`