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What "11" on this clock is supposed to be? it looks like the union symbol but I don't get it.

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2 Answers 2

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It is a union:

$$\bigcup_{n=0}^{10} \{n\} = \{0\}\cup \{1\}\cup\ldots\cup\{10\} = \{0,1,2,\ldots,10\}$$

But then, you take the cardinality of the resulting set: $$ \left\lvert \bigcup_{n=0}^{10} \{n\} \right\rvert = \left\lvert \{0,1,2,\ldots,10\} \right\rvert = 11 $$ and you get $11$, as the set contains $11$ elements.

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  • $\begingroup$ You're too fast, beat me to it! $\endgroup$
    – user409521
    Commented Mar 19, 2017 at 18:55
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    $\begingroup$ @Phyllotactic The joys of being idle on a Sunday. $\endgroup$
    – Clement C.
    Commented Mar 19, 2017 at 18:55
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    $\begingroup$ @MohannadMaklad My personal favorite is this clock. Figuring out the "1" leads to quite an interesting discovery. $\endgroup$
    – Clement C.
    Commented Mar 19, 2017 at 18:58
  • $\begingroup$ Very nice clock! If I want to try and figure it out, could you give me a hint as to what I'm looking for? $\endgroup$
    – user409521
    Commented Mar 19, 2017 at 19:02
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    $\begingroup$ It's related to the prime-counting function. @Phyllotactic $\endgroup$
    – Clement C.
    Commented Mar 19, 2017 at 19:02
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It's the cardinality of the union of all the singlets containing $n$.

So it's the cardinality of the set ${\{0,1,..,10}\}$ which is $11$.

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