In Spivak's Calculus, he provides a """rigorous construction""" of the ordered pair

probably, its been a while since i did anything rigorous

Okay, maybe this is a better way to ask:

Why wouldn't defining (a,b) as {{a},{b}} suffice?

>{{a},{b}}
then (1,2)=(2,1)

The x value is an element of the set containing the x coordinate. The y value is an element of the set containing the y coordinate.

>The definition and accompanying theorem seem arbitrary to me.

That's what makes it rigorous.

Because {{a},{b}} = {{b},{a}}. (Math is not for you. Please study something else, for your own good also.)

And I think you know nothing about teaching or learning.

>it is based on more general primitive notions.
This.
Mathematics is based on set theory.
He formulates [math](a,b)[/math] in set theoretic form using [math]\{[/math] and [math]\}[/math].
From this definition we see that [math](a,b)\neq (b,a)[/math] without using the concept of left and right, but the fact that these are different sets.

>That's what makes it rigorous.
Brainlet.

>Mathematics is based on set theory.
It isn't. This is just the contemporary paradigm.