Linked Questions

0
votes
2answers
163 views

How does the empty set work? [duplicate]

I'm having trouble understanding what exactly an empty set is. Does $\varnothing$ mean $\{\}$ ? and what is the difference between $\varnothing$ and $\{\varnothing\}$ ? If someone could shed some ...
-2
votes
1answer
109 views

Are $\varnothing$ and $\{\varnothing\}$ equal? [duplicate]

Are the sets $\varnothing$ and $\{\varnothing\}$ equal?
1
vote
0answers
74 views

Is the empty set a member of itself [duplicate]

I'm taking Discrete Mathematics and am a little confused on the "empty set" or "null set" defined by ∅. I understand that ∅ is not a member of {∅} but is ∅ a member of {∅, {∅}} given that there is a ...
0
votes
1answer
52 views

can the empty set contain itself? [duplicate]

This question may sound weird but anyway here it goes. Is the following equation true? $$\emptyset = \{ \emptyset \}$$ The reason I think it is not true: The empty set is an element by itself, ...
22
votes
5answers
7k views

Is $\{\emptyset\}$ a subset of $\{\{\emptyset\}\}$?

$\{\emptyset\}$ is a set containing the empty set. Is $\{\emptyset\}$ a subset of $\{\{\emptyset\}\}$? My hypothesis is yes by looking at the form of "the superset $\{\{\emptyset\}\}$" which contains ...
22
votes
8answers
40k 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,...
3
votes
4answers
1k views

Since {} is a subset of every set, it is a subset of itself? and hence {} = {{}}? [duplicate]

I am bit confused with the concept of empty set here. Since {} is a subset of every set, it is a subset of itself? and hence {} = {{}}? Also, say A = {a}, but since {} is a subset of A, is it true ...
2
votes
5answers
420 views

Why is $\{\emptyset\} \not = \emptyset$?

Why is the following true? $$\{ \emptyset \} \neq \emptyset $$ Is it just because the Empty set already refers to there being a set present and so it is just the same argument that $\{ \{3\} \} \...
1
vote
1answer
653 views

What's the successor of $\emptyset$? Do we need to assume that $\emptyset \in \emptyset$ for the successor to exist?

I'm reading Guerino Mazzolla's Comprehensive Mathematics for Computer Scientists 1: Axiom 3 (Axiom of Union) If $a$ is a set, then there is a set $$\{x| \text{ there exists an element } b \in ...
1
vote
2answers
224 views

Is this a set in New Foundations theory of sets: A={x∈X: x∉f(x)} when X=universal set and f(x)=x?

Does the formula A={x∈X: x∉f(x)} define a set in New Foundations theory of sets (NF) when X=universal set and f(x)=x? If not: WHY? It can be seen that many elements of universal set (X) satisfy the ...
0
votes
3answers
78 views

In set notation, why does the meaning of A differ from the meaning of {A}?

If the identity of a set depends on what the set contains, then wouldn't a set represented as A contain the same entities a set represented as {A} contains?
-1
votes
2answers
119 views

Is λ={λ} true or not [closed]

I know that λ={λ} is true I want to know How can I prove that λ={λ} is true or not? Thanks in advance.
0
votes
1answer
48 views

Set theory, equality of sets

Proove or disprove by example If $\{x_1,x_2\}=\{y_1,y_2\}$ then (12) or (21) holds. (12) $x_1=y_1$ and $x_2=y_2$; (21) $x_1=y_2$ and $x_2$=$y_1$. I am mistaking something or could I just set $...