CP 11 Cardinality of Infinite Sets Flashcards
For a graph to be a function it must pass what test
vertical line test
for a function to be bijective it must pass a _______ test and a ______ test
Vertical line
horizontal line
what is the criteria for a function to be surjective
all elements in the codomain must be the image of an element in the domain (y must be a real #)
for a function to be injective it must pass a ____ test
horizontal line
what is the notation for the set of even natural #s
Bolded E
what is an open interval
any (a,b)
Place the following bolded letters in order Eℕℤℚℝ
__⊂__⊂__⊂__⊂__
E⊂ℕ⊂ℤ⊂ℚ⊂ℝ
-note, all these cardinalities are the same because they all have a bijection between them
TF there are many different sets of infinity
T
how do we create a new #
- 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
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
F, we have to show that there exists and injection from one to the other
Given S, we sat S is ______ if |S|= |N|, and its ______otherwise (<,>)
countable
uncountable
what are some examples of countable sets
ℕ, ℤ, and ℚ
What are some uncountable sets
open intervals(a,b) and ℝ
TF for every set S, |S|>|2^S|
F, |S|<|2^S|
TF Given any set, its power set has strictlly larger cardinality
T