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

On 9/22/2024 4:02 AM, FromTheRafters wrote:

Chris M. Thomasson submitted this idea :

On 9/21/2024 4:25 PM, Richard Damon wrote:

On 9/21/24 9:57 AM, WM wrote:

On 21.09.2024 01:06, Richard Damon wrote:

On 9/20/24 2:33 PM, WM wrote:

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How can 10 points exist in linear order without a first one?

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Who says they can't.

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In order to count to 10, you have to start at 1.

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Its just when they become infinite that there might be ends that don't exist.

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In order to count a countable set, you have to start at 1.
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Regards, WM
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Right, so the countable numbers have ONE end that can be used to count from.

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What about the signed integers? Well, we can always start from origin, at 0. ;^)

 You could think of them as a sequence of ordered pairs of naturals.
 ((0,0),(1,0),(1,1),(2,0),(2,1),...)
 First of the pair is the magnitude and the second of the pair is the sign where one equals negation. The sequence is one-ended and perhaps now more obviously countable.
 (0,1,-1,2,-2,3,-3,...)

Agreed. Think of something like:
A = ..., -3, -2, -1, -0
B = +0, +1, +2, +3, ...
(...)A--->(-0+)--->B(...)
Signed zero aside for a moment... lol. ;^)
Make any sense? Or, is it kook ville WM style?
Actually, we can pick any origin we want to. It does not have to be zero...