When Cantor introduced his classification of multiple infinities, he was vehemently rejected by most mathematicians. Ye be warned: contemplating the continuum hypothesis can drive anyone a little mad!

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...

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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