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Cardinality: Level 3 Challenges


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

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

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

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

What is \(|\Bbb Z_2[x]|\)?

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 \(-4,-2,0,2,4,\ldots\).


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