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

On 11/1/2024 7:38 AM, WM wrote:

On 01.11.2024 11:57, FromTheRafters wrote:

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Actual means that all are there,
including the smallest.

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Claims like "The ordinals exists"
work oppositely from how you think they work.
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If I claim "The ordinals exist", then
I don't expand the universe to the ordinals.
I contract our discourse to the ordinals.
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Normally (without magic spells),
talking about stuff doesn't change stuff.
However,
we can change _what we're talking about_
by saying "We're talking about _this_ stuff".
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Here,
you say: the smallest exists.
That does not pop the smallest into existence.
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It contracts our discourse to
lines which have a smallest.
But,
when we look at what else we know about lines,
we also know that _there is no smallest_
You have contracted our discourse to
lines which _do and don't_ have a smallest.
You have contracted our discourse until
nothing exists which we are talking about.
However math.like it sounds,
talk with no referents is gibberish.
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Why?
It is a point on the real line,
well separated from its neighbour.

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You can contract our discourse to
real lines with smallest points,
but they will also be
real lines without smallest points,
which makes our discourse gibberish.
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