sets Flashcards
What is the set of N
the set of natural numbers
{0, 1, 2, 3)
What is the set of Z
the set of integers
…-2, -1, 0, 1, 2…
What is the set of Z+
the set of positive integers
1, 2, 3…
What is the set of Q
the set of rational numbers
{p/q | p ∈ Z, q ∈ Z, and q != 0}
What is the set of R
the set of real numbers
What is the set of R+
the set of positive real numbers
What is the set of C
the set of complex numbers
What does the interval [a, b] mean?
{x | a <= b}
What does the interval [a, b) mean?
{x | a < b}
When are two sets A and B equal?
If they have the same elements i.e. ∀x(x ∈ A ↔ x ∈ B).
What is ∅
The empty set
What is A ⊆ B?
A is a subset of B, i.e. ∀x(x ∈ A → x ∈ B)
How do you show that A is not a subset of B?
Find one element of A that is not an element of B
How do you show that A IS a subset of B?
Show that if x belongs to A then x belongs to B
What is A ⊂ B
A is a proper subset of B, i.e. there is an element x of B that is not an element of A. ∀x(x ∈ A → x ∈ B) ∧ ∃x(x ∈ B ∧ x ¬∈ A)
