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

Question

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

@Karl It can easily be arranged, for $29.50 – Clement C. Mar 19 '17 at 19:00 — Clement C., Mar 19 '17 at 19:00

score 13 · Accepted Answer · answered Mar 19 '17 at 18:54

13

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.

answered Mar 19 '17 at 18:54

Clement C.

67,323

You're too fast, beat me to it! – Mar 19 '17 at 18:55
1

@Phyllotactic The joys of being idle on a Sunday. – Clement C. Mar 19 '17 at 18:55
2

@MohannadMaklad My personal favorite is this clock. Figuring out the "1" leads to quite an interesting discovery. – Clement C. Mar 19 '17 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? – Mar 19 '17 at 19:02
@ClementC. that's pure evil – Mohannad Maklad Mar 19 '17 at 19:02
1

It's related to the prime-counting function. @Phyllotactic – Clement C. Mar 19 '17 at 19:02
Don't understand 1 , 11 and 3 on that clock but I'm working on it! – Karl Mar 19 '17 at 19:05

score 2 · Answer 2 · answered Mar 19 '17 at 18:54

2

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 $11$.

answered Mar 19 '17 at 18:54

Alberto Andrenucci

2,158

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

2 Answers2