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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 - Definition of terminology

If set $$S$$ has $$|S|=3$$ elements and satisfies \begin{align} \text{(i)} &\; 0 \in S \text{ and} \\ \text{(ii)} &\; \text{if } p \in S, q \in S \text{ and } p \neq q, \text{ then } (p+q) \in S \end{align} and $$10$$ is an element of $$S,$$ what is the other element of $$S$$ excluding $$0$$ and $$10?$$

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If $$A$$ is the set of all odd positive integers less than $$50,$$ what is the number of elements in $$A?$$

If $$A$$ is the set of all integers satisfying $$11 \leq x \leq 27,$$ what is the number of elements in $$A?$$

If $$A$$ is the set

$A= \{13, 17, 9, 0, -13\},$

what is $$\lvert A \rvert?$$

Details and assumptions

You may choose to read the summary page Set Notation.

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

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