>What if aliens have no notion of discrete numbers, what if everything is probabilistic analog math? 0 and 1 are both valid probabilities. >What about an orga

>What if aliens have no notion of discrete numbers, what if everything is probabilistic analog math? 0 and 1 are both valid probabilities. >What about an organism that can see/focus/sense multiple things simultaneously, and a single "thing" is a set. Its possible, using sets only containing other sets (or possibly the empty set), to construct the integers. >There could be an entirely different paradigm to "counting" and consequently to the fundamentals of maths. Systems of mathematical expressions are just like coding languages. The choice is arbitrary, one can always emulate the job of another. Just like how I did with your chosen examples, in principle one can always hack the integers out of whatever system you give me (or hack whatever system out if integers).