# What is $\left|\bigcup\limits_{n=0}^{10}\{n\}\right|$ supposed to be?

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

• I want that clock.
– Karl
Commented Mar 19, 2017 at 18:58
• Commented Mar 19, 2017 at 19:00

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.

• You're too fast, beat me to it!
– user409521
Commented Mar 19, 2017 at 18:55
• @Phyllotactic The joys of being idle on a Sunday. Commented Mar 19, 2017 at 18:55
• @MohannadMaklad My personal favorite is this clock. Figuring out the "1" leads to quite an interesting discovery. Commented Mar 19, 2017 at 18:58
• 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?
– user409521
Commented Mar 19, 2017 at 19:02
• It's related to the prime-counting function. @Phyllotactic Commented Mar 19, 2017 at 19:02

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 $11$.