# Math Help - Is it true that x = {x} ?

1. ## Is it true that x = {x} ?

Is it true that 2 = {2} ? (Where {2} is the set containing just 2)

If not why is this the case?

Furthermore can we say that 2 E {{2}}?

Thanks

2. ## Re: Is it true that x = {x} ?

Originally Posted by kinhew93
Is it true that 2 = {2} ? (Where {2} is the set containing just 2)
If not why is this the case?
Furthermore can we say that 2 E {{2}}?
$2\ne\{2\}~$. $~2$ is a natural number and $\{2\}$ is a set containing the number $2$.

$2\notin\{\{2\}\}$

Some axiomatic systems do define:
$\\0=\emptyset\\1=\{0\}\\2=\{0,1\}\\3=\{0,1,2\}\\ \vdots$ See Halmos.

3. ## Re: Is it true that x = {x} ?

Hello, kinhew93!

Are you really this confused on basic Set theory?

Is it true that 2 = {2}? .(Where {2} is the set containing just 2) .No
If not, why is this the case?

We have $2$.
This is like having a banana.

We have $\{2\}$.
This is a paper bag containing a banana.

These are not the same.

Furthermore can we say that: . $2 \in \{\{2\}\}\,?$ .No
[
$2$ is a banana.

$\{2\}$ is a bag containing a banana.

$\{\{2\}\}$ is a bag containing a bag containing a banana.

We can say: . $2 \in \{2\}\,\text{ and }\,\{2\} \,\in\,\{\{2\}\}$

. . . and that's all.

4. ## Re: Is it true that x = {x} ?

Thanks - i know its simple I was just checking exactly what the notation meant, eg is it like a bag containing a banana or just a 'group' of one banana. thanks for clarifying

5. ## Re: Is it true that x = {x} ?

Originally Posted by kinhew93
Thanks - i know its simple I was just checking exactly what the notation meant, eg is it like a bag containing a banana or just a 'group' of one banana. thanks for clarifying
No, that is not the question you asked. A 'bag containing a banana' is NOT a banana but neither is "a 'group' of one banana". A "group" or "set" or "collection" of one thing is NOT that thing.