9.1 Bijections Flashcards
1
Q
What is a injective function
A
1-1 mapping
2
Q
What is a surjective function
A
Spans entire codomain
3
Q
What is a bijective function
A
4
Q
What is an isopmorphic function
A
Has an inverse
5
Q
What are the 2 identity functions in relation to f and f^-1
A
6
Q
What is the relationship between a bijective function and an isomorphic function
A
Imply each other (iff)
7
Q
What is an example bijection between integers and natural numbers
A
Pos => even
Neg => odd
8
Q
How to prove that something is a bijection
A
- Prove injective (k1 = k2)
- Prove surjective (any b has a corresponding a)
9
Q
How to prove that something is an isomorphism
A
Construct an inverse function and prove both IDs
