A thought I had:
Many people think that n/infinity = 0 (where n is a finite value), and I used to agree with this, until today.
Imagine a universe where there are an infinite variety of particles, and that every square of area in the universe was filled with a random combination of any of these particles. If n/infinity = 0, then each area is filled with nothing as there is a 0% chance of every combination of particles to exist there.
That to me is paradoxical, how can something be filled with infinite physical objects yet have nothing inside of it?
#does n/infinity really equal 0?
vagrant python
supple grove
A thought I had:
Many people think that n/infinity = 0 (where n is a finite valu...
countably infinitely many particles?
if you are distributing countably many particles uniformly over countably many volumes (which is already not possible mathematically) then thats inf/inf, not n/inf
vagrant python
No, not like that. Each area has a finite amount of particles but the combination at which these particles are distributed in that area is random and can be made of any of the infinity particles.
supple grove
No, not like that. Each area has a finite amount of particles but the combinatio...
oh, so it’s more like infinitely many elements
we have a square and we place some finite amount of atoms on it in random places
vagrant python
We aren't doing it, the universe is
supple grove
and your argument is that this is paradoxical because for any layout of atoms, there was a 0% chance of that happening?
vagrant python
According to those who think n/infinity = 0, it is 0%, yes it is paradoxical
supple grove
lets make the thing simpler
choose a random number between 0 and 1
for whatever number you picked, the chance you picked it is exactly 0
and yet the total chance of picking a number is 1
seems paradoxical, but it works out
because probability of uncountable disjoint union is not necessarily given by adding up all the probabilities
you can think about assigning each area the probability a point will be picked in it
now, as the area gets smaller, this chance should go to 0
but instead we can think about dividing that probability by the area, we may get something positive for the limit
and then we get total probability with an integral
frosty surge
Isn't it n/inf approaches 0? Which, in the OP's question, is functionally different to equal 0? We can round it to zero, we can mostly use it as zero, but it isn't actually zero.
tropic thunder