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

On 10/11/2024 12:48 PM, Ross Finlayson wrote:

On 10/10/2024 09:22 PM, Jim Burns wrote:

What I mean by 'first transfinite ordinal' ω is that,
of all ordinals which are not.finite,
ω is the first such ordinal.
>
What I mean by 'ordinal' is that
each set of ordinals holds a minimum or is empty.
>
What I mean by 'finite ordinal' γ is that
it is first (ie, γ=0) or
its predecessor.ordinal γ-1 exists and,
for each non.0 prior ordinal β<γ
its predecessor.ordinal β-1 exists.

The mathematical objects of
a strong mathematical platonist's mathematical universe
are _discovered_, not _invented_.

What effect does discovery.not.invention or
invention.not.discovery have?
I don't see any effect. What do you see?

and for strong mathematical platonists
these are the words we use for
"infinite-dimensional vector spaces":
infinite-dimensional vector spaces.

⎛ In mathematics and physics,
⎜ a vector space (also called a linear space) is
⎜ a set whose elements, often called vectors,
⎜ can be added together and multiplied ("scaled")
⎜ by numbers called scalars.
⎜ The operations of vector addition and scalar multiplication
⎝ must satisfy certain requirements, called vector axioms.
⎛ A subset of a vector space is a basis if
⎜ its elements are linearly independent and
⎜ span the vector space.
⎜ Every vector space has at least one basis,
⎜ or many in general.
⎜ Moreover,
⎜ all bases of a vector space have the same cardinality,
⎝ which is called the dimension of the vector space.
https://en.wikipedia.org/wiki/Vector_space
I am familiar with words like those for
"infinite.dimensional vector spaces".
They apparently aren't any different
for Platonists or for formalists.

and for strong mathematical platonists
these are the words we use for
"infinite-dimensional vector spaces":
infinite-dimensional vector spaces.

I don't see what point you are driving towards.