#set theorists

[then-ponder]

Set theorists what is your preferred set notation?

Preferred set notation

{Expression : Rule}

{Rule : Expression}

Voting ended onMay 23, 2024

{Expression : Rule} is the form of{2n : n ∈ ℕ} and is formally expressed as “the set of all thing of the form 2n such that n is an element of ℕ”.

{Rule : Expression} is the form {n ∈ ℕ: 2n} and is formally expressed as “the set of all n in ℕ such that 2n”

[todays-xkcd]

"The Venn diagram of the sun and the moon is a circle." --someone being snarky at totality

Overlapping Circles [Explained]

[thingswicked]

Attention Set Theorists!

I'm taking a class that deals with Set Theory, and I find some of the assumptions utterly perplexing.  The theory we are learning is ZFC-(that minus sign should be superscript).

I have questions.

Assumption 4: Union - If A is a set, then there is a set whose members are those sets which are members of some member of A.  (In 'Mathese' - For all x, there exists some y such that, for all z, z is a member of y iff there exists w such that w is a member of x and z is a member of w.)  I don't understand what this means.  If anyone has a less abstract example or a diagram that is helpful, that would be much appreciated.

Assumption 5: Powerset - If A is a set, then there is a set whose members are the subsets of A.  (For all x, there exists y such that, for all z, z is a member of y iff z is a subset of x.)  I don't understand why A is different that the powerset of A.

If anyone has ANYTHING of use that helped them learn this, PLEASE message me.  If you feel really helpful and want to explain anything extensively, then message me and I will give you my email address.