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:

[...]

>
Actual means that all are there,
including the smallest.

Claims like "The ordinals exists"
work oppositely from how you think they work.
If I claim "The ordinals exist", then
I don't expand the universe to the ordinals.
I contract our discourse to the ordinals.
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".
Here,
you say: the smallest exists.
That does not pop the smallest into existence.
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.

Why?
It is a point on the real line,
well separated from its neighbour.

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.