Re: Replacement of Cardinality

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?