[d--b]

This is mathematics, not physics. You can define stuff that don't "really" exist in the world, but that work for the purpose of calculating stuff.

"randomness" has as much right to exist in a mathematical sense as a "point" or a "plane".

[thfuran]

Randomness exists in physics as well.

[d--b]

I am just responding to the comment which assumes that it doesn't.

[_8j50]

How can you prove something that isn't real? How is randomness defined as a concept in mathematics?

[siver_john]

As long as you can clearly define your starting axioms you can mathematically prove or disprove anything. The physical example would be to just say, suppose a universe with the same properties of ours exist but where the gravitational constant is twice as large prove whether X can occur in that universe.

As far as how randomness is defined I believe that might be field dependent but this is me getting out of my depth (I've only taken a few courses on combinatorics).

[DavidSJ]

Randomness is usually defined in terms of a probability distribution, which is just a measure where the total mass assigned to all elements adds up to 1.

[majkinetor]

You can actually only prove unreal things because you impose limitations. Real things can not be proven, but only disproved.