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Probability

Set Notation

Concept Quizzes

Sets - Definition of terminology
Sets - Subsets
Sets - Classical Sets
Sets - Problem Solving

Challenge Quizzes

Set Notation: Level 2 Challenges
Cardinality: Level 3 Challenges

Cardinality: Level 3 Challenges

In terms of cardinality, are there more rational or irrational numbers?

Since there are infinitely many rational as well as irrational numbers, it cannot be determined Irrational Numbers Both are equal in number Rational Numbers

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by Nihar Mahajan

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The number of "Figure 8's" that you can draw in a plane such that they do not cross each other is...

Finite Uncountably Infinite

(\beth_1)

Countably Infinite

(\aleph_0)

Doubly Uncountably Infinite

(\beth_2)

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by Daniel Liu

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Do there exist uncountably many subsets of the natural numbers such that every pair of the subsets has finite intersection?

No Undecidable in ZFC Yes

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by Ivan Koswara

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Let $\Bbb Z_2[x]$ denote the set of polynomials with integer coefficients modulo 2.

What is $|\Bbb Z_2[x]|$ ?

\aleph_1

Uncountable Infinite Finite

\aleph_0

Countably Infinite

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by A Former Brilliant Member

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True or False?

The cardinality (size) of the set of natural numbers $1,2,3,\ldots$ is same as the as the cardinality (size) of the set of even numbers $-4,-2,0,2,4,\ldots$ .

False True

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by Yash Dev Lamba

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