The Kuratowski Construction of Ordered Pairs

[@k.v.krishnateja2553]

From time ( 9:00 to 9:40 mins ) in your video, you talked about how the pairing axiom is used to create the four sets depicting the four cartesian products and how the union axiom is used to fit these two sets into a super set A X B, but if we use the union axiom, aren't we creating a super set which just has all the elements from the four sets rather than four elements, each having two elements? In other words, shouldn't the cardinal number be 8 when we use the pairing axiom and then the union axiom rather than four as it was shown in this video? And if we do want the result shown in the video, shouldn't we use the pairing axiom twice and then the union axiom? I hope I'm not asking too much by this comment but I really liked your video and I really want an answer to this.

[@elliotnicholson5117]

You use the subset axiom to create the 4 sets which represent the ordered pairs. Then the oairing axiom to put them inside sets. Then union all those sets together.

[@k.v.krishnateja2553]

@@elliotnicholson5117 , thank you. I didn't read your reply properly at first but I get it now.

[@johnthescott2409]

i have never seen a generalization to AxBxC.

[@Jop_pop]

Fyi the title of this video has a typo

[@elliotnicholson5117]

Thank you

[@BlackEyedGhost0]

(3,3) = 5 {{3}} = {4} Seems like a silly unintended consequence.

[@هيلة-ع8م]

But they’re just “names” for the sets, they (still) don’t have any meaning, once they do, then (based on the context) you can use what ever notation that fits