Re: How many different unit fractions are lessorequal than all unit fractions?

On 9/8/24 3:48 PM, WM wrote:

On 07.09.2024 16:49, Richard Damon wrote:
 

All those add up to less than x, so they fit.
Select any gap between one of the first ℵo unit fractions and its

neighbour. Call its size x. Then ℵo unit fractions cannot fit into the interval (0, x), independent of the actual size.
 Regards, WM
 

But that is changing the value of x in the middle of the problem which isn't allowed.
Given that new x, we can choose a new set of Aleph_0 unit fractions below that x.
It seems your mind can't grasp the concept of infinite sets, which allow sets of the same cardinality to have one be the subset of the other.
Yes, that would just blow the mind that is stuck in finite logic, where that doesn't work.
That is why we get strangeness of things like x + 1 can be equal to x, as adding one to Aleph_0 doesn't change its value