added some open circles

I adjusted H to use heaviside's 1/2 convention, good catch.

https://en.wikipedia.org/wiki/Limiting_density_of_discrete_points

log(infinite number) seems a promising avenue of investigation. also reminiscent of harmonic series--in euler's words-- its sum is the log of an infinite number. 

Skipping context sure saved me a lotta time, and plus you gave a nice elab

shoe thrifting is meh for me because foot size

What sort of boots?

Where to get shoes: Meermin

Ivan Karamazov ranting to his brother Alyosha about basically a cabal watching over the world, thought of herenow

From Goldblatt, since {0..H} is internal.

Gonna sleep bc 3 am but will respond later. Also the remark that hyperfinite can mean smaller than a nonstandard natural just seems false, where did you get that idea from?

I used compactness in recent comment reply. Hypernaturals are uncountable because they are bigger than all the nats and so can’t be counted. Whether cardinality of continuum is equivalent to continuum hypothesis

I thought about this since. Bigger is not the right word. Complicated maybe? Like how the unit interval contains non-measurable sub intervals, or a compact set contains non-compact subsets.