/sci/ - Science & Math

>>11334724
>Is the universe expanding at the same rate in every direction?

It appears to be, yes. The appearance that Earth was dead center of the expansion was a major tell that the expansion was actually of space itself, and not objects fleeing a central point.

Are the number of digits in .999... countable or uncountable? What would happen if you used the "wrong" infinity.

If you can't answer this question, how can .999... have any meaning at all?

>>8782054
>"What is the probability that the second moon orbiting earth will explode?"

That one is actually LESS absurd. It's probability is not even zero because something definable as a second moon might exist someday and then explode. (I don't think "moon" is all that strictly defined, so a satellite might count - and someone could have named one "second moon".

But getting back to the original point, you have these two different situations. "Can't happen" and "can happen with zero probability" that can't be explained with real numbers. To me, it is the second, not the first, that is absurd. But it becomes simple if you say that the chance of the RNG producing .5 is an undefined infinitesimal.

> So it doesn't matter if 0.9999... and 1 are _exactly_ the same, they lie in the same equivalence class* and we use "=" to denote this. Therefor 0.9999... = 1

I expect this is probably true, but it makes the Real set a totally inappropriate tool to discuss the equivalence of 0.9999... = 1. None of these "proofs" prove anything because the Real set is defined to exclude the very subject that is being discussed. It's like proving that all cars have the same top speed by using a racetrack that enforces a speed limit.