One of the most counterintuitive aspects of modern mathematics is that everything within it is built upon the precise definitions made by mathematicians. What's even more counterintuitive is that mathematicians can actually revise some definitions within mathematics.
This is because one of the most fundamental and crucial principles of modern mathematics is logical consistency, or rationality.
To put it in layman's terms: no matter how outrageous your definition may be, as long as within a mathematical system all theorems and derivations are based upon a set of accurately defined axioms, and these derivations and conclusions are not mutually contradictory, then it is considered correct.
It can formally exist within mathematical definitions.
For instance, a quintessential example is the definition of the imaginary unit: i^2 = -1.
