2.1 Set Concepts Flashcards

1
Q

Set

A

Collection of objects (ex: United States)

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2
Q

Elements ∈

A

The objects in a set (ex: the 50 states of the United States)
∈ meaning “element of”

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3
Q

Well-defined

A

Contents can clearly be determined (ex: set of US)

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4
Q

Not well-defined

A

Contents cannot be clearly determined (ex: the best movies on Netflix)

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5
Q

What are the 3 methods used to indicate a set?

A

Description, roster form, set-builder notation

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6
Q

Description

A

Ex: Write a description of the set containing Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday

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7
Q

Roster form

A

List the elements of a set inside a pair of brackets (ex: {1, 2, 3, 4,…, 10})

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8
Q

Set-builder notation

A

Used to symbolize a set (ex: E = {𝑥|𝑥 ∈ 𝑁 𝑎𝑛𝑑 𝑥 > 10})

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9
Q

Inclusive

A

Includes the numbers stated in roster form (ex: set of natural numbers between 5 and 20 inclusive is {5, 6, 7, 8, …, 20})

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10
Q

Finite

A

Either contains no elements or the number of elements in the set is a natural number (the set ends)

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11
Q

Infinite

A

The set is not finite (ex: {1, 2, 3, …})

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12
Q

How can two sets be equal?

A

If they contain elements that are exactly the same, regardless of order (ex: {2, 4, 6} = {4, 2, 6})

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13
Q

How can two sets be equivalent?

A

If both sets’ cardinal numbers are the same (ex: {1, 2, 3} is equivalent to {red, yellow, orange})

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14
Q

Cardinal number 𝑛(𝐴)

A

The number of elements in a set

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15
Q

One-to-one correspondence

A

Every element of set A can be matched with exactly one element set B

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16
Q

Empty (or null) set { } or ∅

A

A set that contains no elements

17
Q

Universal set (U)

A

A set that contains all the elements for any specific discussion (only the universal set may be used in that problem)

18
Q

Natural number (N)

A

A positive whole number

19
Q

Ellipses

A

… to signal a set continuing