term1 Definition1term2 Definition2term3 Definition3
Please sign in to your Google account to access your documents:
Relation
Given sets A and B, we say that R, which is a subset of A x B, is a relation from A to B.
Equivalence Relation
A relation R on A x A is called an equivalence relation if it reflexive, symmetric, and transitive.
Equivalence Class
Given an equivalence relation R on A x A, we define the equivalence class of a in A to be the set
[a] = {b in A | aRb}.
Function
Given the sets A and B, the relation R from A to B is said to be a function if for each a in A there exists a unique b in B such that aRb.
Injective
Let f:A->B. We say that f is injective if for all a, a' in A we have that f (a)=f (a') implies a=a'.
Surjective
Let f:A->B. We say that f is surjective if for all b in B there exists an a in A such that f (a)=b.
Right Inverse
Let f:A->B be given. We say that g:B->A is a right Inverse of f if f (g (b))=b for all b in B.
Left Inverse
Let f:A->B be given. We say that g:B->A is a left Inverse of f if g (f (a))=a for all a in A.
Need help typing ? See our FAQ (opens in new window)
Please sign in to create this set. We'll bring you back here when you are done.
Discard Changes Sign in
Please sign in to add to folders.
Sign in
Don't have an account? Sign Up »
You have created 2 folders. Please upgrade to Cram Premium to create hundreds of folders!