Why is pic related true/false? Set theory

Because green is true. green excludes red.

>>8212660
You could ask yourself: can a set contain itself?

Elements aren't defined by a set containing only themselves. A set can contain sets. A set can contain colors or flavors of laffy taffy. A color isn't a set that contains itself.

Saying 'by definition' about something you don't understand doesn't make it true. In reality, real numbers are often constructed via sets and relations on these sets--however, they are not just a single set with a lone element plucked out.

>>8212660
Maybe just because A = {A} isn't explicitly defined. Because {A} is a proper subset of {A,B,C}.

>>8212666
So informally put, A != {A} because "{A}" has been defined as a set where as "A" is just the lone "number" ?

First of all, A = {A} is never true, due to the axiom of regularity.

Secondly, I don't know where you pulled the black text from, but it's stupendously false. Don't quit your day job.

>>8212701
someone told me the black text was true so I thought it was true

>>8212660
I think I'm reading this right
https://en.wikipedia.org/wiki/Axiom_of_regularity

>>8212703
Stop thinking that, and maybe take some time out of your day to call that person an idiot.

>>8212660
Think of a set like a bag. If you write out the things in the bag, you wouldn't include the bag. The things in the bag are the elements.

How can A = {A} if {A} includes lambda by virtue of being a set

>>8212694
If you are assuming ZFC, then that is a formal theorem. No set contains itself.