section 2.1: sets

Question 1

what is a set?

Answer 1

an unordered set of objects

Question 2

what are elements?

Answer 2

the objects in a set

Question 3

what will a set usually consist of?

Answer 3

numbers

Question 4

what is the notation for a set?

Answer 4

a capital letter
ex: A, B

Question 5

what is the notation for an element?

Answer 5

a lowercase letter
ex: a, x

Question 6

what does a (\in ) A mean?

Answer 6

the element a is an element in set A

Question 7

what is the notation for an empty / null set?

Answer 7

∅ or {} or {∅}

Question 8

what does the symbol ∀ mean?

Answer 8

for every element

Question 9

what is cardinality?

Answer 9

the size of a set that does not include repeated elements

Question 10

what is the notation for cardinality?

Answer 10

|A|

Question 11

when are two sets equal?

Answer 11

if there exists sets A and B such that ∀x <–> x (\in ) B

Question 12

what does ∀x <–> x (\in ) B mean?

Answer 12

for every element in A, that element belongs to B, and for every element in B, that element is also in A

Question 13

a set A is called a subset of B if:

Answer 13

∀x –> x (\in ) B

Question 14

what is a proper subset?

Answer 14

a subset A ⊆ B, where B has additional elements, denoted A C B

Question 15

what is the notation for a subset?

Answer 15

A ⊆ B

Question 16

what is the notation for a proper subset?

Answer 16

A C B

Question 17

do the elements have to appear in the same order for a set A to be equal to or a subset of B?

Answer 17

no, the order the elements appear in does NOT matter

Question 18

is a proper subset a subset?

Answer 18

yes

Question 19

is a subset a proper subset?

Answer 19

no

Question 20

can a set be infinite?

Answer 20

yes

Question 21

can a set be finite?

Answer 21

yes

Question 22

can one set have elements of different varieties (number, fruit, animal)?

Answer 22

yes

Question 23

what is the cardinality of the null (empty) set?

Answer 23

zero

Question 24

what is the set of natural numbers, ℕ?

Answer 24

the set of all numbers that is greater than or equal to zero

Question 25

what is the symbol for the set of natural numbers?

Answer 25

ℕ

Question 26

is zero included in ℕ?

Answer 26

yes

Question 27

what is the set represented by this symbol, ℤ?

Answer 27

the set of all integers, from -infinite to +infinite

Question 28

what is the set represented by ℤ^+?

Answer 28

the set of all positive integers, starting from one {1, 2, 3, 4, …}

Question 29

what is the set represented by ℤ^-?

Answer 29

the set of all negative integers, starting from
negative one {-1, -2, -3, -4, …}

Question 30

what is IR?

Answer 30

the set of all real numbers