Sujet : Re: How many different unit fractions are lessorequal than all unit fractions? (repleteness)
De : james.g.burns (at) *nospam* att.net (Jim Burns)
Groupes : sci.mathDate : 17. Sep 2024, 21:11:25
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <1b54c6c9-8b85-4c59-865a-fb601eaf4e1f@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
User-Agent : Mozilla Thunderbird
On 9/17/2024 2:57 PM, Ross Finlayson wrote:
On 09/17/2024 10:59 AM, Jim Burns wrote:
[...]
>
I do seem to recall that
your account was around when it was set out,
for example,
that least-upper-bound is nice neat trivial next,
In ℕ and ℤ
there are integers next to each other,
which is to say,
there are integers with no other integers between.
In ℚ
there are no rationals next to each other,
because
there are no rationals with no rationals between.
In ℝ
there are no reals next to each other,
because,
however close |x-y| = d > 0 is,
there are no d.sized gaps in the rationals,
so there must be rationals between.
The least.upper.bound of (0,1) is 1
but 1 isn't next to any element of (0,1)
Unlike ℕ and ℤ, ℚ and ℝ do not 'next'.
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