Sujet : Re: How many different unit fractions are lessorequal than all unit fractions?
De : james.g.burns (at) *nospam* att.net (Jim Burns)
Groupes : sci.mathDate : 20. Sep 2024, 20:51:01
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <298dcb6f-5f58-48b6-80e3-34260bf721f8@att.net>
References : 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
User-Agent : Mozilla Thunderbird
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.
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