Week 2 Lecture - set Flashcards
What is a set?
a collection of elements.
x ∈ S
x is an element in set S.
What is the simplest way of describing a set?
Stating its elements. e.g.
Does the order of the listing of the set matter?
no - {H,d,c} and {d,h,c} are describing the same set
What does it mean if sets have the same elements?
The sets are equal, i.e. A=B.
Are sets {1,1,2} and {1,2} equal?
Yes.
Are sets {2} and {{2}} equal?
No.
What does the set Z describe?
the infinite set of integers
What does the set N describe?
the set of natural numbers.
What does N+ describe?
set of positive integers.
what does Q describe?
set of rational numbers - m/n, where m and m don’t equal 0
What does R describe?
All rational and irrational numbers.
How do you describe sets by recursion?
3 steps :
(1) Basis step : specify one or more elements of S
(2) Recursive step : give more rules to construct new elements of S from existing elements of S.
(3) Exclusion rule: state that S consists only of the elements specified by the basis step or generated by the recursive.
Example of describing a set by recursion.
The set |N can be described recursively:
Basis step 0 ∈ N
Recursive step if n ∈ N , then n+1 ∈ N
