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

On 10/11/2024 4:48 PM, Ross Finlayson wrote:

On 10/11/2024 11:02 AM, Jim Burns wrote:

⎜ the typical “working mathematician” is
⎜ a Platonist on weekdays and a formalist on Sundays.

I'm familiar with that you tend to repost that,
yet platonism and formalism don't necessarily
contradict nor preclude each other, with regards
to neither necessarily being fictionalism.

About what mathematics *IS*
there is disagreement between mathematicians, and
sometimes even between the same mathematician
on different days.
About what mathematics *SAYS*
there isn't _that kind_ of disagreement.
⎛ When I gather my Authority about me
⎜ in order to Proclaim a Truth,
⎜ it's nearly always what mathematics *SAYS*
⎜ The times I Proclaim what mathematics *IS*
⎝ I have goofed and mis.stated opinion as knowledge.

Mathematics is not "pretend",

On the other hand, we all know that
you will never dig up a square root in your garden.
Yes,
mathematics follows rules.
However, lots of "pretend" follows rules, too.
Consider vampires, garlic, etc.
Yes,
when mathematics answers a question,
we are well.advised to pay attention.
However, the same is said for the best of "pretend":
Shakespeare, Aesop, and their ilk.
If mathematics is not "pretend",
please tell me the difference between
mathematics and "pretend".

and it's in accords to
some ultimate ontological commitment
to the _truth_ of the mathematical _facts_,
not "make-believe".

"Aristotle

"Zeno

"Cantor

"Russell

Frege

Anaximander

Goedel

Cohen

I couldn't find where you or these others say
what it is which
you or they _mean_ by "make-believe".

some ultimate ontological commitment
to the _truth_ of the mathematical _facts_,

⎛ In professional wrestling, kayfabe (/ˈkeɪfeɪb/) is
⎜ the portrayal of staged events within the industry
⎜ as "real" or "true", specifically the portrayal of
⎜ competition, rivalries, and relationships between participants
⎜ as being genuine and not staged.
⎜ The term kayfabe has evolved to also become
⎜ a code word of sorts for maintaining this "reality"
⎝ within the direct or indirect presence of the general public.
[1]
Compare and contrast: mathematical fact, kayfabe.
[1]
https://en.wikipedia.org/wiki/Kayfabe