So, first of all I'm gonna start with stating that I'm a complete noob in mathematics that started doing this as a hobby. I encounter problems that I can't figure out on a regular basis, like a few times per page but I usually find someone to help me. This time those same people were of no help so I came here.
We have an ordered pair $(a,b)$, okay?
And if we wanted to show the world that ordered pair using set theory it would look like this: $\{\{a\},\{a,b\}\}$.
Yeah, I don't get that at all. As I've came to understand in the ordered pair order does matter. So how come it doesn't look like this when using set theory: $\{\{a\},\{b\}\}$? I know my question is probably retarded but this seems awfully confusing to me. How come the second coordinate can be either a or b? Logic makes me believe that my previous way of thinking can't be true and that I'm understanding it completely wrong. Can someone help me with this using simple language?
Improvements: Now I understand why $\{\{a\},\{b\}\}$ doesn't apply. Thanks for the first step helpers.