math question

[careful]

so the empty set is the set which contains no elements. its assumed to exist and then its pretty easy to show that its unique. the empty set is a subset of any set, which im guessing might be an alternative way to define the empty set, as the unique set that is a subset of any and every other set (what do you think?). but is it a subset of itself?

Spoiler

im pretty sure the answer is yes. since every element of the empty set is a member of the empty set (the definition of a subset), even though there in fact happens to be no elements.it still conforms to the definition of a subset.

Spoiler

am i right?

edit: but that cant be right! cuz the empty set has no elements so it doesnt have any subsets! im confused now....

 

[Draconalis]

No elements, assumed to exist, unique...

Are we talking about God?

 

[Glademaster_v1legacy]

Firstly you kinda messed up the spoiler tag. Then this [http://wiki.answers.com/Q/Is_an_empty_set_is_a_subset_of_empty_set] might be useful.

 

[SckizoBoy]

It all depends on how the sets are defined, but 'properly', no, an empty set is not a subset of itself, largely because there's the problem of equal sets. Thus, it's impossible to have two empty subsets within a set, regardless of how it's... layered (sorry, I don't do set theory). This is how an empty set can be a subset of any set, but it cannot be a subset unto itself.

Thus, you're wrong, by virtue of there being a lack of elements within said set, therefore, it cannot have subsets... hell, you've answered your own question!

Stop making my head hurt!

 

[Knife]

so the empty set is the set which contains no elements. its assumed to exist and then its pretty easy to show that its unique. the empty set is a subset of any set, which im guessing might be an alternative way to define the empty set, as the unique set that is a subset of any and every other set (what do you think?). but is it a subset of itself?

Spoiler

im pretty sure the answer is yes. since every element of the empty set is a member of the empty set (the definition of a subset), even though there in fact happens to be no elements.it still conforms to the definition of a subset.

Spoiler

am i right?

edit: but that cant be right! cuz the empty set has no elements so it doesnt have any subsets! im confused now....

Spoiler

Spoiler

Yes the empty set is subset of itself, every set is subset of itself. Think about it that way - the empty set A is a subset of empty set B because there is no element of A that cannot be found in B (pretty much the same definition for all other sets which also works for the empty set).

 

[careful]

so the empty set is the set which contains no elements. its assumed to exist and then its pretty easy to show that its unique. the empty set is a subset of any set, which im guessing might be an alternative way to define the empty set, as the unique set that is a subset of any and every other set (what do you think?). but is it a subset of itself?

Spoiler

im pretty sure the answer is yes. since every element of the empty set is a member of the empty set (the definition of a subset), even though there in fact happens to be no elements.it still conforms to the definition of a subset.

Spoiler

am i right?

edit: but that cant be right! cuz the empty set has no elements so it doesnt have any subsets! im confused now....

Spoiler

Spoiler

Yes the empty set is subset of itself, every set is subset of itself. Think about it that way - the empty set A is a subset of empty set B because there is no element of A that cannot be found in B (pretty much the same definition for all other sets which also works for the empty set).

Spoiler

Spoiler

ah! yes thank you! that makes sense

 

[Knife]

ah! yes thank you! that makes sense

Glad to be of service.
Finally the semester on Discrete Math put to good use...

 

[Wekub]

Aye, as above.
But note that you can have a set containing the empty set which is not the empty set.
Think of the empty set Ø = {} as an empty box.
Such a set S containing the empty set would then be S = {Ø} = {{}}, i.e. a box containing an empty box.
Then again, I might be messing this up and it's defined as the opposite. But I don't think so.
G'night.

 

[ShindoL Shill]

I hate math but let's see if I understand what you're asking, does an empty set contain itself?

Don't worry, Pinkie Pie is on it!

nooo pinkie! if you divide by 0 then...
the calculator says MATH ERROR! and you feel bad.

OT: i suppose... it doesnt contain anything... and sets contain a specified group of numbers. logically, an empty set wouldnt contain any sets... but a set could contain itself...
in-sets-ion.