Week%201

# Week%201 - Supplement to Week 1 0.1 Sequences and functions...

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Supplement to Week 1 January 24, 2007 0.1 Sequences and functions Let A be any set and let n be a natural number. Recall that A n stands for the set of ordered n-tuples of the form ( a 1 , a 2 , . . . , a n ), where each a i is an element of A . Here the order matters, so for example if n = 3 and A = { a, b, c } , then ( a, a, b ) is different from ( a, b, a ). Thus an ordered n-tuple of elements of A is just a sequence of n elements of A . This exactly the same thing as a function from the set { 1 , . . . , n } to the set A . Namely, to specify such a function, one just has to specify its value a i at each i = 1 , . . . n . If you have trouble with this, take n = 3 and A = { a, b, c } and try writing down all (or some) of the functions from { 1 , 2 , 3 } to A and then all (or some) of the sequences ( a 1 , a 2 , a 3 ) ∈ A 3 . More generally, if S and A are any sets, we can consider the set A S := F ( S, A ) of all functions from S to A . If S and A are finite, can you find a formula...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online