/sci/ - Science & Math

somethings been bothering me.

as we divide 1 by larger and larger numbers. it gets smaller.
lets divide 1 by 2^n as n approaches infinity
the presumed result will be 0

But if we look a little closer and start asking some questions things get funny.

in order for 1/2^n to reach zero it has to go through a certain threshold. Imagine you have a sieve that only things that are 1 centimetre can pass through, you could strain materials for an infinite amount of time but nothing wider than 1 centimetre will ever pass through.

in order for 1/2^n to be zero there has to be a number A that is passed through but pass through it leads to problems because we must pass from positive to 0 while dividing by 2. the point between positive and zero is where the sieve lies and it only lets through numbers with certain properties a number must have the property A/2 = 0 and a > 0 to pass through this sieve, it has to be greater than 0 because it is coming from the positive direction.

if you don't pass through the sieve than 1/2^n can't equal 0

but it is impossible to pass through the sieve because the properties a number needs to have to pass through the sieve are impossible.

why does everyone pretend this isn't a problem?

1. Some infinities bigger than other infinities

2. let A and B represent different sized infinities. A > B

3. C = 0.999... such that (...) = A. D = 0.999... such that (...) = B


C > D