Linked Questions

7
votes
3answers
1k views

Subsets of sets containing empty set [duplicate]

Why is $\{\emptyset\}$ not a subset of $\{\{\emptyset\}\}$? It contains this element, but why is it not a subset?
3
votes
6answers
266 views

Why $\{ \emptyset \} $ is not a subset of $\{ \{\emptyset \} \} $ [duplicate]

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) $\...
2
votes
5answers
313 views

Why is $\{\emptyset\}\not\subseteq\{\{\emptyset\}\}$ true? [duplicate]

My book "Introduction to SetTheory" says $\{\emptyset\}\in\{\{\emptyset\}\}$ but $\{\emptyset\}\not\subseteq\{\{\emptyset\}\}$ When we say $\{\emptyset\}\not\subseteq\{\{\emptyset\}\}$, we mean ...
1
vote
0answers
101 views

Why $\{\emptyset\} \not \subset\{\{\emptyset\}\}$? [duplicate]

In my text book it is written that: { } ⊆ { }; { } ⊆ {0/}; { } ⊆ { {0/} }; { } ⊆ C; and {0/} ⊆ C; { {0/} } ⊆ C; but ...
88
votes
3answers
22k views

Construct a function which is continuous in $[1,5]$ but not differentiable at $2, 3, 4$

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 ...
30
votes
8answers
51k views

Is the empty set a subset of itself?

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,...
12
votes
4answers
16k views

Empty set does not belong to 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 $, ...
-2
votes
3answers
1k views

Are the following statements true?
“{∅} = ∅” ?
“{∅} ⊃ ∅”?

Are the following statements true? 
“{∅} = ∅” ?
 “{∅} ⊃ ∅” ? Stumbled upon this question. Was wondering what the answer was. Could you guys explain in return?
5
votes
2answers
154 views

Is $\{\{\emptyset\}\}$ actually a set?

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 ...
1
vote
1answer
1k views

Is “{x}” or “x” a member of the set {x,y,z}?

I'm getting a little confused with sets and subsets. Which of the following is a member of {x,y,z}? "x" or {x}?
2
votes
3answers
413 views

Why does the curly bracket do not equal to the double curly brackets?

$\{a\} \neq \{\{a\}\}$ $\{a\}$ 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 '...