Is $x\in\{\{x\}\}$

Question

Is $x\in\{\{x\}\}$. I understand that $x\in\{x\}\in\{\{x\}\}$ does this mean $x\in\{\{x\}\}$?

Very simple just unsure about the properties of $\in$, not looking for an extravagant answer, thanks in advance for the help.

score 3 · Accepted Answer · answered Dec 23 '14 at 17:18

3

The answer is no. $\{\{x\}\}$ has exactly one element, namely $\{x\}$.

In general, to test if $a\in b$, we do the following:

$a$ can be a set itself, or not, doesn't matter.

answered Dec 23 '14 at 17:18

vadim123

3

And $x\neq {x}$, by the axiom of regularity. – Jonas Meyer Dec 23 '14 at 17:19
2

Even without AR, so long as $x\neq {x}$ for ANY $x$, the conclusion fails to hold. – vadim123 Dec 23 '14 at 17:23

score 2 · Answer 2 · answered Dec 23 '14 at 17:19

2

The answer is no. Good analogy is list in programming language Python.

answered Dec 23 '14 at 17:19

Jihad

2 Answers2