Do mathematicians possess any evidence in support of the existence of arbitrary union sets?

[Boojatta]

Poll question: Do mathematicians possess any evidence in support of the existence of arbitrary union sets?

In other words, do mathematicians possess any evidence in support of the following claim?

If m is any set, then there exists a set u such that for all x, x is an element of u if and only if there exists y such that x is an element of y and y is an element of m.

For example, the binary union operator applied to two sets a and b results in the set u that we get above if m is the unordered pair {a,b}.

[Ian David]

1. Please un-freep this poll on arbitrary union sets...

http://tinyurl.com/67kocc

[TreasonousBastard]

2. Is this about gay marriage?

[Boojatta]

3. No. Nor is it about trade unions.

It's about the things known as sets or collections.

[RobertSeattle]

5. I like Trade Winds

[RobertSeattle]

4. You forgot Poland.

[amdezurik]

6. Ok, you first 3 choices include no option for

it has been us3ed for a long time now withoug contradiction, but as soon as one comes up adjustments will be made, and applications explored for the exception(s). I am sure the implication in all 3 of those choices of matmaticians being resistant or openly hostile to challenges to assumptions is accidental but it does seem to be an inditment of mathmaticians...

[Glorfindel]

7. Evidence?

What more evidence could we need?

[jgraz]

8. All three!

[Lucky 13]

9. You needed one more option in your poll:

This question is completely over my head and I have no idea what the fuck you are talking about.

:hi:

[edhopper]

10. But do

mathematicians like buttercream frosting on their cupcakes?

[Boojatta]

11. Kick

[ColbertWatcher]

12. Bah! Everyone knows the answer is ...

... too big to post in the margin!

[Jim__]

13. You need to clarify the question.

If m is any set, then there exists a set u such that for all x, x is an element of u if and only if there exists y such that x is an element of y and y is an element of m.

This sounds very much like an axiom of Zermelo-Fraenkel, the Axiom schema of specification, with u = y.

Outside of Zermelo-Fraenkel, the claim is not always true. For instance, in a set theory that allows for urelements, let m be a set all of whose elements are urelements. Then, the claim that x is an element of y is meaningless when y is an element of m.

[TechBear_Seattle]

14. Set theory is just mental masturbation

Although a useful form of mental masturbation, granted.

Set theory, abstract algebra, most of calculus, algebraic theory, numeric analysis... all of got their start with someone saying "Just suppose...." Mathematics is a branch of logic and an expression of abstract thought; it is not a "hard" science with evidence and testable results like physics or geology or chemistry.

Your question is meaningless (as so many of your questions are.)

[ZombieHorde]

15. Is evidence required for arbitrary things? For example,

the types of doughnuts I enjoy are arbitrary to my example, does my example require evidence that I enjoy certain types of doughnuts?