/sci/ - Science & Math

Why don't you find out yourself?

yes

is 0 in the empty set?

If you assume the empty set contains the empty set, then the empty set is non-empty.

Christ are you THAT retarded?

>>5575708
You are an idiot.
Saying that the empty set contains the empty set doesn't mean that the empty set is not empty.
It would be non-empty if there were an element lying in it. "Containing is a relation between two sets. "Lying" is a relation between an element and a set.

The answer is obviously yes. Every set contains itself, so the empty set contains itself as well.

>>5575708

but if the empty set is empty, then the empty set within the empty set wouldnt violate the first set being empty.

See the one thing I hate about philosophy these days is that all the good points are so well defined and put to their use that they're not even given credit anymore
>Monetary system
>Zero
>Using fire

BUT IS ZERO IN THE EMPTY SET?

The empty set is a subset of every set. The empty set is not an element of every set.

if every set contains the empty set, and the empty set contains the empty set, then every empty set contains another empty set.

Shit, the turtles go all the way down.

>>5575735
but to be a subset it must be an element.

>>5575702
>>5575731
I'll award a Millenium prize to the first person who can answer this.

it does not contain zero. zero is an element.

>>5575740
For a set to be a subset of another, every element in it must also be in the other.

It is true that every element in the empty set is in every other set. Because it's empty.

>>5575749
No.

every set does NOT contain the empty set. are you fucking stupid?

>>5575757
>>5575756
Thanks. You can both share Perelman's Millennium prize - he didn't want it for some reason.

The empty set is a subset of every set. Your wording can be misinterpreted.

Contain needs to be defined.

A set can contain an element, and a set can contain a subset. But it's two distinct uses of the word contain.

Use precise language: If every set has the empty set as a subset, is the empty set a subset of itself? The answer is yes.

>>5575683
The empty set is a subset of itself, but not an element of itself.

For example, given A = {B, {C}}. B is an element of A and so is {C}. But C is not an element of A.

>>5575855
but to be a subset it must also be an element.

The empty set is a subset of every set... that doesn't mean it's an element of every set.

>>5575924
>but to be a subset it must also be an element.

except for the empty set, because.... its empty.

Is the sum of the set containing only zero is greater than the sum of the empty set?

>>5575935
What the hell is the "sum" of a set?

>>5575937
I guess he means the sum of the elements.

>>5575937
According to the Wikipedia the sum of set S is <span class="math">\sum_{x\in S} x[/spoiler]

>>5575942
I figured. It doesn't make any sense though. What is the sum of {0,4,{2,3},{1,{2}},5}?

>>5575954
4 + {2, 3} + {1, {2}, 5}

THE ANSWER IS NO!, NO! NO! NO! NO! NO!

straight from the mouth of my math professor, "the set that contains only the empty set is not the empty set". It therefore stands to reason that the empty set does not contain itself.

Is a box containing an empty box empty?

>>5575957
That's a nonsensical expression.

>>5575683
Nope.
{}∈{} =>{{}}⊆{}
But |{{}}|=1 whilst |{}|=0. But right frrom the off, the idea that {} is in {} implies there is something in {} which contradicts its definition... so itt is incorrect to say all sets contain the empty set. It's like saying, if all natural numbers are greater than 1, then is 1 great er than 1? The claim is wrong. You should conclude that not all sets contain the empty set... the empty set is a subset of all sets however.

Not OP, but if the empty set is a subset of every set, wouldnt it violate the definition of the complement of a set that originally contained the empty set?

>>5575723
>the empty set within the empty set wouldnt violate the first set being empty.
According to the rules of grammar.
But not the rules of math.

sage for troll

>>5577151
The complement of a set does not contain the empty set. Your argument is invalid.

Also, go fuck yourself.

This is like a typical problem in any Topology/Analysis/Set theory textbook. To be specific...

Is the empty set a subset of itself? Yes. This follows directly from the definition. It just so happens that this is a vacuous truth since the empty set contains no members.

Is the empty set a member of the empty set? No; it is not an object/element. Do not confuse member/element relationships with set relationships. Like I said, this is basic stuff learned in the first week of a class in mathematical logic/set theory.

>>5575683
vacuous truth mother fucker.

>if every set contains the empty set

Every set does not contain the empty set.

The Empty set looks like this {}
The set containing the empty set looks like this { {} }

>>5578524
jesus not this fucking thread again.

There is nothing in the empty set. That is why it is empty.
There is, however, the set of the empty set, which is non-empty.
Think of it as putting an empty box into an empty box.
The outer box is no longer empty.

>>5578619
it is if the box doesnt count as a something. just like a set doesnt count as something unless there is shit in it.

>>5575702
0 is not in the empty set because 0 has a value of 0x31.

MILLENIUM PRIZE PLEASE.

>>5578621
Well, you could say that.
If you wanted to be wrong, that is.
The set of the empty set is non-empty because it has an element: the empty set.

an intersection of several sets does not mean that the intersection contains itself

>>5578626
Son, do you hear yourself?

The empty set contains itself because it is empty.

>>5578628
That's not even what I was talking about, but okay.

>>5578626
you are one contradictory motherfucker.

>>5578628
But that's a contradiction.

How many elements does the empty set contain? (Hint: 0).

>>5578639
the empty set contains no elements. Therefore it can be within the empty set because it does not violate the condition that it be empty.

>>5578646
I think you are getting confused. The empty set is a subset of every set, not an element of every set.

>the empty set contains no elements
Exactly.

>>5578650
to be a subset it must also be an element.

>>5578653
By that logic, the empty set contains infinite elements.

I am beginning to realize I am being trolled.

The empty set has measure zero, we can ignore it and move on with our lives.

>>5578653
You're confused.

A={1,2,3}, B={1}. B is a subset of A, but {1} is not an element of A.

>>5578653
areyoufuckingserious

>>5578698
>>5578674
>>5578663

you are being trolled.