>>171
Real numbers are equivalence classes of Cauchy sequences of rational numbers.
No they are not only. There is only one set unique up to isomorphism satisfying each of the following properties:
A. It is a totally ordered field.
B. Addition and multiplication are defined. Each element except zero has a multiplicative inverse. Etc.. Addition and multiplication tie into the ordering...
B.1. if x > y then x + z > y + z
B.2. if x > 0, y > 0, then xy > 0
C. Every non empty subset that is bounded admits a least upper bound.
The rationals pass A and B, but fail C. The integers pass A and C, but only 1 and -1 have multiplicative inverses, so they fail B.
https://en.wikipedia.org/wiki/Real_number#Axiomatic_approach
But it takes at least one construction to validate their existence.
Rational numbers are constructed from the integers.
Yes, as equivalence classes of Z*Z.
Integers are constructed using formal logic.
Hah!
Formal logic can be used to disprove your idiotic kike bullshit.
Hah! Seriously, while I've found the bullshit to be idiotic since Nikita started spamming /prog/, I stopped arguing with him once I realized it was impossible to prove that a conspiracy didn't exist, regardless of any connotations for the said conspiracy.
Therefore you should oppose real numbers.
no