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

On 9/20/2024 2:24 PM, WM wrote:

On 19.09.2024 20:31, Jim Burns wrote:

On 9/19/2024 6:38 AM, WM wrote:

Either there is a point next to zero
or there is no point next to zero,

>
Consider ABCDEFGHIJKLMNOPQRSTUVWXYZ
>
Q is between A and Z
A and Z are not next to each other.
>
Nothing is between P and Q
P and Q are next to each other.
>
⎛ There is a gap between P and Q

>
No.

There is no letter between P and Q
in ABCDEFGHIJKLMNOPQRSTUVWXYZ
There is an absence of letters between P and Q
in ABCDEFGHIJKLMNOPQRSTUVWXYZ
There is a gap between P and Q
in ABCDEFGHIJKLMNOPQRSTUVWXYZ

⎜ A gap isn't some _presence_
⎜ A gap is an _absence_ of whatever.

>
A gap in the real line is the absence of points.

A gap between 0 and x is
the absence of points between 0 and x
No point x exists for which
there is an absence of points between 0 and x

Consider the real line.
For any two points x and y,
(x+y)/2 is between x and y.
x and y are not next to each other.

>
That is true for definable points only.

For points u and v at splits Sᵤ and Sᵥ of ℚ
point (u+v)/2 is between u and v.
u and v are not next to each other.