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# Set Notation

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!

# Sets - Classical Sets

If $$\mathbb{R}$$ denotes the set of real numbers, and $$S$$ is the set

$S = \{ 7, 1+\sqrt{2}, \pi, \sqrt{-11}, -11, 0, (-6)^3, -\sqrt[3]{2} \} ,$

how many elements does $$\mathbb{R} \cap S$$ have?

Details and assumptions

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If $$\mathbb{Q}$$ denotes the set of rational numbers, and $$S$$ is the set

$S = \{ 9, 1+\sqrt{2}, \pi, \frac{5}{19}, \sqrt{-14}, -9, 0, (-6)^3, -\sqrt[3]{2} \} ,$

how many elements does $$\mathbb{Q} \cap S$$ have?

Details and assumptions

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How many positive integers are there in the set

$\{ x \mid -14 \le x < 66\}?$

How many negative integers are there in the set

$\{ x \mid -15 \le x < 37\}?$

How many elements are in the set $$\{10, 12, 14, \ldots, 48, 50\}$$?

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