section 2.1: sets Flashcards
lecture 1
what is a set?
an unordered set of objects
what are elements?
the objects in a set
what will a set usually consist of?
numbers
what is the notation for a set?
a capital letter
ex: A, B
what is the notation for an element?
a lowercase letter
ex: a, x
what does a (\in ) A mean?
the element a is an element in set A
what is the notation for an empty / null set?
∅ or {} or {∅}
what does the symbol ∀ mean?
for every element
what is cardinality?
the size of a set that does not include repeated elements
what is the notation for cardinality?
|A|
when are two sets equal?
if there exists sets A and B such that ∀x <–> x (\in ) B
what does ∀x <–> x (\in ) B mean?
for every element in A, that element belongs to B, and for every element in B, that element is also in A
a set A is called a subset of B if:
∀x –> x (\in ) B
what is a proper subset?
a subset A ⊆ B, where B has additional elements, denoted A C B
what is the notation for a subset?
A ⊆ B
what is the notation for a proper subset?
A C B
do the elements have to appear in the same order for a set A to be equal to or a subset of B?
no, the order the elements appear in does NOT matter
is a proper subset a subset?
yes
is a subset a proper subset?
no
can a set be infinite?
yes
can a set be finite?
yes
can one set have elements of different varieties (number, fruit, animal)?
yes
what is the cardinality of the null (empty) set?
zero
what is the set of natural numbers, ℕ?
the set of all numbers that is greater than or equal to zero
what is the symbol for the set of natural numbers?
ℕ
is zero included in ℕ?
yes
what is the set represented by this symbol, ℤ?
the set of all integers, from -infinite to +infinite
what is the set represented by ℤ^+?
the set of all positive integers, starting from one {1, 2, 3, 4, …}
what is the set represented by ℤ^-?
the set of all negative integers, starting from
negative one {-1, -2, -3, -4, …}
what is IR?
the set of all real numbers
