Sets - Classical Sets

         

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

S={7,1+2,π,11,11,0,(6)3,23}, S = \{ 7, 1+\sqrt{2}, \pi, \sqrt{-11}, -11, 0, (-6)^3, -\sqrt[3]{2} \} ,

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

Details and assumptions

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

S={9,1+2,π,519,14,9,0,(6)3,23}, S = \{ 9, 1+\sqrt{2}, \pi, \frac{5}{19}, \sqrt{-14}, -9, 0, (-6)^3, -\sqrt[3]{2} \} ,

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

Details and assumptions

You may choose to read the summary page Set Notation.

How many positive integers are there in the set

{x14x<66}? \{ x \mid -14 \le x < 66\}?

How many negative integers are there in the set

{x15x<37}? \{ x \mid -15 \le x < 37\}?

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

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