Just to explain myself perhaps a little better. Set theory since at least the mid 19th century has been fundamental to the basis of mathematics. The natural nu

Just to explain myself perhaps a little better. Set theory since at least the mid 19th century has been fundamental to the basis of mathematics. The natural numbers are defined starting fromthe empty set and a successor operation that given a set a returns a U {a}, then the integers are defined as infinite sets of pairs from the cartesian product of the natural numbers with a particular common property[1], and rationals as infinite sets of pairs of integers[2]. Then Dedekind constructed the reals from the rationals and proved the least upper bound property. His construction is essentially to cut the numberline of the Rationals into two sets with specific properties (but essentially one less than and one greater than or equal to a particular real number, with the lower set having no largest element). There is an excellent pair of youtube videos explaining how number systems are defined using sets https://youtu.be/dKtsjQtigag?si=3JFgz2YTUqB7EAv3 https://youtu.be/dKtsjQtigag?si=3JFgz2YTUqB7EAv3 and https://youtu.be/IzUw53h12wU?si=D0lx1vCiy5FwjlwC https://youtu.be/IzUw53h12wU?si=D0lx1vCiy5FwjlwC [1] Which you could think of as being that everything in the set [(a,b)] has a-b equal to some common integer which is what we think of as that particular integer. So the set [(2,0)] contains (2,0), (4,2) (-4,-6) and so on to infinitiy in both directions and that entire set of pairs we think of as the integer “2” [2] where the common property is a division rather than a subtraction