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

Am 19.09.2024 um 21:13 schrieb Chris M. Thomasson:

On 9/19/2024 5:55 AM, WM wrote:

On 18.09.2024 22:49, Moebius wrote:

Am 18.09.2024 um 21:35 schrieb Chris M. Thomasson:

On 9/18/2024 5:44 AM, WM wrote:

On 16.09.2024 03:16, Richard Damon wrote:

On 9/15/24 3:39 PM, WM wrote:

On 15.09.2024 18:38, Ben Bacarisse wrote:
>

It might be worth pointing out that any non-trivial interval [a, b] on
the real line (i.e. with b > a) contains an uncountable number of
points.

>
That proves that small intervals cannot be defined (they are dark).

>
But arbitrary small intervals CAN be defined.

For any eps e IR, eps > 0: [0, eps] is an interval (@WM: you see, I just defined it) of length eps and it countains an uncountable number of points. Hint: eps may be arbitrarily small, as long as it is > 0.

Try to name one that can't.

>
Define an interval comprising 9182024 points, starting at zero.

>
There IS NO "interval comprising 9182024 points", hence NOTHING TO DEFINE HERE, you fucking asshole full of shit.

>
How can infinitely many points be accumulated without a first one?

@WM: There's no need for them "to be accumulated" (whatever this may mean), you fucking asshole full of shit.

The real line is infinitely long

WM is talking about some interval of finite length here, it seems.

and infinitely dense, or granular if you will...

Sorta.