Sujet : Re: Replacement of Cardinality
De : chris.m.thomasson.1 (at) *nospam* gmail.com (Chris M. Thomasson)
Groupes : sci.logic sci.mathDate : 13. Aug 2024, 20:25:41
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <v9gbvl$1g5h$10@dont-email.me>
References : 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
User-Agent : Mozilla Thunderbird
On 8/10/2024 4:00 PM, Moebius wrote:
Am 11.08.2024 um 00:52 schrieb Chris M. Thomasson:
On 8/10/2024 3:47 PM, Moebius wrote:
Am 11.08.2024 um 00:40 schrieb Chris M. Thomasson:
On 8/10/2024 8:59 AM, WM wrote:
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The set of unit fractions has two ends, namely at 1 and before 0.
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They have no end
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Nope. They have an end at 1/1.
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Well, I needed to give more context. 1/1, in my mind makes me think of the first, [...]
Again, 1/1 is the first term in the sequence (1/1, 1/2, 1/3, ...), but it's the largest/last unit fraction in respect to < (as defined on IR, and hence on the unit fractions).
... < 1/3 < 1/2 < 1/1.
In the other hand the first term of (1/1, 1/2, 1/3, ...) is 1/1, the second is 1/2, etc.
Actually, the most important lesson is taught here:
See: https://www.youtube.com/watch?v=VScSEXRwUqQ
Please study it closely!
It depends on context. Are we going from 1/1 all the way down, or from 0/1 all the way up to 1/1. 0/1 is not a unit fraction, which means there is no smallest one... Fair enough?
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