Comment by Gehinnn

> Irrational numbers are defined as any numbers that cannot be written as a ratio of two integers.

> Finally, the set of real numbers, denoted R, is defined as the set of all rational numbers combined with the set of all irrational numbers.

I'm sorry, this is not how math works. Reals are basically defined as number. But what is a number?

Also the definition of Q is missing the quotient construction (or any motivation of how to deal with ka/kb = a/b).