CP 11 Cardinality of Infinite Sets Flashcards

1
Q

For a graph to be a function it must pass what test

A

vertical line test

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2
Q

for a function to be bijective it must pass a _______ test and a ______ test

A

Vertical line
horizontal line

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3
Q

what is the criteria for a function to be surjective

A

all elements in the codomain must be the image of an element in the domain (y must be a real #)

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4
Q

for a function to be injective it must pass a ____ test

A

horizontal line

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5
Q

what is the notation for the set of even natural #s

A

Bolded E

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6
Q

what is an open interval

A

any (a,b)

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7
Q

Place the following bolded letters in order Eℕℤℚℝ
__⊂__⊂__⊂__⊂__

A

E⊂ℕ⊂ℤ⊂ℚ⊂ℝ

-note, all these cardinalities are the same because they all have a bijection between them

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8
Q

TF there are many different sets of infinity

A

T

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9
Q

how do we create a new #

A
  • apply each number into ur fomrula which results in different numbers,
  • go down each rational number and choose column by column different number than whats there to get ur new number
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10
Q

TF in terms of infinite cardinalitites, if the cardinality of one set is ≤ the cardinality of another set then we just have to show there exists a surjection from 1 to the other

A

F, we have to show that there exists and injection from one to the other

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11
Q

Given S, we sat S is ______ if |S|= |N|, and its ______otherwise (<,>)

A

countable
uncountable

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12
Q

what are some examples of countable sets

A

ℕ, ℤ, and ℚ

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13
Q

What are some uncountable sets

A

open intervals(a,b) and ℝ

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14
Q

TF for every set S, |S|>|2^S|

A

F, |S|<|2^S|

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15
Q

TF Given any set, its power set has strictlly larger cardinality

A

T

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16
Q
A