Question

Is this true? ∅ is a subset of {∅, {∅}}

Answer 1

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Answer 2

i think \(\phi\) is a subset of any set
and here, \(\{\phi\}\) is also a subset

Answer 3

can people explain to me what {∅, {∅}} means?

Answer 4

in the first case it is used as empty set,
in the second case it is used as an element

Answer 5

@kropot72 correct me if im wrong

Answer 6

is it: empty set is a subset of ... (dont know this part)
Why do they use {{∅}}?

Answer 7

\(\phi\) represent an empty set.
\(\{\phi\}\) here, \(\phi\) is an element with in a set
\(\{\{\phi\}\}\) here, \(\phi\) is an element with in a subset of set

Answer 8

but they all mean empty sets... :(?

Answer 9

It is accepted in mathematics that each set is a subset of itself. It is also accepted that the empty set is a subset of every set.

Answer 10

\(\{\phi\}\) is this an empty set ?
i dont think so... i may be wrong...

Answer 11

so this question is True?

Answer 12

its true.

Answer 13

but im confused with my question above lol

Answer 14

so can you use english to translate all the symbols please?

Answer 15

The empty set is denoted by the symbol\[\phi\]

Answer 16

so is it "empty set is a subset of two elements an empty set and an element of an empty set"...?

Answer 17

yep ! thats correct translation of ur question.

By definition,
"empty set is a subset of any set"

Answer 18

so no matter how they write it, it will always be true?
Like {∅} is a subset of {∅, {∅}}
and {{∅}} is a subset of {∅, {∅}}

Answer 19

no wait a sec.. they all are different things i think. pls wait.

Answer 20

@kropot72 u have handy knowledge on this...

Answer 21

The empty set is a member of every set, including itself. This is fundamentally true.

Answer 22

second line she has put also true ?

Answer 23

for the second line, is that because in one of the element in the list is {{∅}} ? so {{∅}} is in the list?

Answer 24

yep.. second line is also true. that element is in list.
u are using it correct :)

Answer 25

so should I treat ∅ as an variable like X or something? Do they have the same properties?

Answer 26

\(\{\{\{\phi\}\}\}\) is not a subset

Answer 27

nope \(\phi\) is a set

Answer 28

Like {∅} is a subset of {∅, {∅}}
and {{∅}} is a subset of {∅, {∅}}
I agree that the first line is true but cannot get my head around the second line. The question is an extreme example of set theory anyway. I would not push it further myself:)

Answer 29

me too lol :)

Answer 30

lol I have {{∅}} do not equal {∅} on my notes
maybe I will ask my professor tomorrow morning..

Answer 31

yep they are not equal

Answer 32

\(\phi\) is a set
\(\{\phi\}\) is also a set, but its not empty. it has ONE element

Answer 33

\(\{\{\phi\}\}\) is also set, that contans ONE subset, which contains ONE element.

Answer 34

i may be completely wrong... pls other guys pitch in n correct me :\

Answer 35

@pog8207215 thats what i think... i think its correct.
does it make sense to u ?

Answer 36

thank you for the explanation ! It makes so much more sense to me that way!

Answer 37

I have a question that has real numbers...

Answer 38

glad to hear that.. :))