Linked Questions

Why is $\{\emptyset\}$ not a subset of $\{\{\emptyset\}\}$? It contains this element, but why is it not a subset?

Following are two statements from Enderton's book on set theory, I fail to understand that if empty set is a subset of every set then why can't it be a subset of $\{ \{ \emptyset \} \} $ (1) $\...

My book "Introduction to SetTheory" says $\{\emptyset\}\in\{\{\emptyset\}\}$ but $\{\emptyset\}\not\subseteq\{\{\emptyset\}\}$ When we say $\{\emptyset\}\not\subseteq\{\{\emptyset\}\}$, we mean ...

In my text book it is written that: { } ⊆ { }; { } ⊆ {0/}; { } ⊆ { {0/} }; { } ⊆ C; and {0/} ⊆ C; { {0/} } ⊆ C; but ...

Construct a function which is continuous in $[1,5]$ but not differentiable at $2, 3, 4$. This question is just after the definition of differentiation and the theorem that if $f$ is finitely ...

Sorry but I don't think I can know, since it's a definition. Please tell me. I don't think that $0=\emptyset\,$ since I distinguish between empty set and the value $0$. Do all sets, even the empty set,...

Herbert in his book "Elements of set theory" on page no 3 says that we can form the set $ \{ \emptyset \} $ whose only member is $\emptyset $. Note that $ \{ \emptyset \} \neq \emptyset $, ...

Are the following statements true? 
“{∅} = ∅” ?
 “{∅} ⊃ ∅” ? Stumbled upon this question. Was wondering what the answer was. Could you guys explain in return?

I think this question is not asked here. I apologize in advance if I am wrong. I have the following two definitions (Joaquín Olivert, Estructuras de álgebra multilineal, 1996): Class.- A class is an ...

I'm getting a little confused with sets and subsets. Which of the following is a member of {x,y,z}? "x" or {x}?

$\{a\} \neq \{\{a\}\}$ $\{a\}$ is the set whose only element is the a (and no others). $\{\{a\}\}$ is the set whose only element is the set $\{a\}$. Does this mean the 'element a' is not equal to '...