Question

Translate this to english and say whether its true or false :
∀ X ∈ P(N), X ⊆ R

Answer 1

@myininaya

Answer 2

For every x is an element of the set P(N), x is a subset of the set R.

Answer 3

That is how I read it.

Answer 4

I'm not sure what set R represents and what set P(N) represents.

Answer 5

well i don't know how to make the power set symbol on this.

Answer 6

its powerset(N)

Answer 7

R represents real number

Answer 8

what does N represent

Answer 9

naturals?

Answer 10

Natural numbers yes

Answer 11

So do you know what the powerset of the naturals look like?

Answer 12

We will use the notation you defined here since I don't know how to make the powerset symbol either

Answer 13

or the double back R or N

Answer 14

\[N=\left\{ 1,2,3,4,... \right\}\]

Answer 15

what is subset and what is powerset ? i never really understood that lol

Answer 16

\[P(N)=\left\{ \emptyset , \left\{ 1 \right\} , \left\{ 1,2 \right\},\left\{ 1,2,3 \right\},..., N\right\}\]

Answer 17

basically a powerset is a set that list all of the possible subsets

Answer 18

so the list I just wrote out is all the possible subsets of the natural numbers

Answer 19

P({1,2,3})
={emptyset, {1},{2},{3},{1,2},{1,3},{2,3},{1,2,3} }
You know you listed them all when you have listed 2^number of elements

Answer 20

Like in that example there are 3 elements in {1,2,3}
so there are 2^3 subsets of {1,2,3}

Answer 21

Do you understand what a subset and a powerset is? And what the difference is?

Answer 22

Like I just gave the powerset of {1,2,3} above
all the sets listed in that set are subsets of {1,2,3}
--
emptyset subset of {1,2,3}
{1} subset of {1,2,3}
{2} subset of {1,2,3}
{3} subset of {1,2,3}
{1,2} subset of {1,2,3}
{1,3} subset of {1,2,3}
{2,3} subset of {1,2,3}
{1,2,3} subset of {1,2,3}

Answer 23

is empty set basically just the number 0 ? thanks for your explanation btw im actually just taking it all in right now so sorry i havent responded lol

Answer 24

{ } is the set containing nothing
there are no members (not even the member 0

Answer 25

hmm okay..

Answer 26

{0} is the set containing 0

Answer 27

but 0 is something

Answer 28

not nothing

Answer 29

i know that sounds weird

Answer 30

right

Answer 31

lol

Answer 32

like you can say { } or emptyset or use that little symbol I used before

Answer 33

\[\emptyset \]

Answer 34

so basically the question is asking you if all the members of the powerset of the natural numbers is also a subset of the the real numbers

Answer 35

the members of the powerset are the subsets of the natural numbers
like the empty set is a member of the powerset of the natural numbers
the {1} is a member of the powerset of the natural numbers
{2} is a member of the powerset of the natural numbers
{1,2,3,4,5} is a member of the powerset of the natural numbers
N is a member of the powerset of the natural numbers

Answer 36

so true ?

Answer 37

I think I could do a better yep

Answer 38

\[P(\mathbb{N} )=\left\{ \emptyset, \\ \left\{ 1 \right\} , \left\{ 2 \right\},...,\\ \left\{ 1,2 \right\} , \left\{ 1,3 \right\}, \left\{ 1,4 \right\},..., \\ \left\{ 1,2,3 \right\},...,\\ \mathbb{N} \\ \right\}\]

Answer 39

It is impossible to list all of those sets
but you get the point I think

Answer 40

Yes lol, Thanks!!