Chapter 2 - Sets, Functions, Sequences, Sums, Matrices Flashcards

1
Q

Two sets are equal …

A

if and only if they have the same elements

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2
Q

set

A

unordered collection of objects, “contains” its elements

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3
Q

elements or members

A

objects in a set

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4
Q

roster method

A

S = {a, b, c, d ….}

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5
Q

set builder notation

A

SetName = {variable | condition}

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6
Q

Sets: N

A

Natural numbers: N = {0, 1, 2, 3, …}

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7
Q

Sets: Z

A

Integers: Z = {…, -2, -1, 0, 1, 2, ….}

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8
Q

Sets: Z+

A

Positive Integers: Z+ = {1, 2, 3, …}

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9
Q

Sets: Q

A

Rational Numbers: Q = {p/q | p ∈ Z, q ∈ Z, q ≠ 0}

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10
Q

Sets: R

A

Real Numbers

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11
Q

Sets: R+

A

Positive Real Numbers

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12
Q

Sets: C

A

Complex Numbers

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13
Q

∈, ∉

A

is an element of, is not an element of

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14
Q

A is a subset of B, A ⊆ B …

A

if and only if every element of A is also an element of B

A ⊆ B

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15
Q

Empty or Null Set

A

A set that contains no elements

Ø or { }

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16
Q

Singleton Set

A

A set with on element

{1}, {Ø}, {a}, etc.

17
Q

Cardinality

A

The number of distinct elements (n)

|S|

18
Q

Power Set

A

the set of all the subsets of the set

P(S)

19
Q

Ordered n-tuple

A

the ordered collection (a1, a2, … an)

ordered 2 tuples are called ordered pairs

20
Q

Cartesian product (A x B)

A

The set of all ordered pairs (a, b) where a ∈ A and b ∈ B

A x B = {(a, b) | a ∈ A ^ b ∈ B}

21
Q

A U B, Union

A

the set that contains those elements that are either in A or in B or in both

22
Q

A ∩ B, Intersection

A

the set that contains those elements in both A and B