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

On 10/29/2024 08:15 AM, Jim Burns wrote:

On 10/28/2024 2:53 PM, Ross Finlayson wrote:

On 10/28/2024 11:31 AM, Jim Burns wrote:

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[...]

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Of course you would mean
"finite ordinals as
a brief summary model of discernibles the members" of
"the closure of all relations that make things numbers,
all those sets, too, all the related things",
"the" "numbers".

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I mean finite ordinals as finite ordinals.
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Ordinals are well.ordered:
each set of them holds a first or is empty.
Each ordinal has its successor.
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Each finite ordinal has its predecessor or is 0  and
each of its prior ordinals has its predecessor or is 0
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Natural numbers, whole numbers, rational numbers,
real numbers, complex numbers, algebraic numbers,
transcendental numbers...
I find the term "number" problematic until
the description of _which_ numbers is given.
And, once given the description,
we reason from the description,
and ignore where "number" is used.
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If the term "number" evaporated,
I would not greatly miss it.
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Most people observe an extensionality in
the "real-valued", then for example somebody like
Hardy also relates real-valued values to points
on a line.
The complex "numbers" don't really have a distinct
definition of division, so, they're not really unique.
Of course "numbering" and "counting" may be
two different things.
When you say "finite ordinals" what's intended
is "all the body of structural relation with
regards to the ordinal and with regards to the
finite", and it's doens't necessarily say so
much about "the numbers" or even "the natural
numbers", as with regards to that Peano's numbers
aren't merely zero and a closure to successor,
there's constant monotone increase and modularity,
and some have it's only where the operations of
the addition and division, semi-groups, come together.