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I am confused on these questions I feel like that are too easy. I just need to find the cardinality of each of the 3 problems. I believe that the first one and third one is a zero with a slash through it. Then the second question I believe is 3. Can anyone veryify this for me please.

  1. $\{ x \colon x \in \mathbb{R} \text{ and } x^2=2 \}$

  2. $\{a,b , \{a,b\} \}$

  3. $\{x \colon x \in \mathbb{Z} \text{ and } x^2=2 \}$

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  • $\begingroup$ what about $\sqrt{2}$? $\endgroup$ – dafinguzman Feb 19 '14 at 8:12
  • $\begingroup$ Number 3 is the empty set; its cardinality is $0$ (zero), not $\emptyset$ (the empty set). $\endgroup$ – TonyK Sep 30 '14 at 9:49
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The first one has two elements in it: \begin{equation} \{x \ |\ x\in\mathbb{R}, x^2=2\}=\{\sqrt 2, -\sqrt 2\}\end{equation} so its cardinality is 2.

The second set has 3 elements in it so its cardinality is 3 and finally the last one is the empty set so its cardinality is zero.

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