Just a story on how you can come up with ideas. A bit like philosophy.

Say you have a universe where you only have an add() function. Then what infinity objects could this universe have?

Assuming the universe have time. Then conquer up an idea object that would give you some similarity to the infinity idea.

So to get something non countable with the add() function. I imagine you use the add function like a counter in loop. Then you can just speed up the add process.

Pretty soon the number result will become unreadable or unrecognizable. Like a stop watch this will go towards something unrecognizable.

So you have some speed limit of recognition.

Then beyond the limit. I think you will have the situation that the add function will add to the number it can not recognize.

So this sounds like a random number which then is just an unrecognizable. Therefor it is independent to the time sample function.