My website: alok.blog.
Alok Singh
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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.
Each number gets infinitesimal weight. Which infinitesimal is basically arbitrary.
iLate reply, but the slicker bit is going in more fully. The appeal of the NSA approach here is axiomatizing it which helps people understand because people already know what numbers are, so ‘inf big’ is much less of a stretch than going the usual crazy inference depth math has.
This really benefits from a picture. Calling something “a nonstandard number” doesn’t really convey anything about them and a better name I’ll use is “infinitely big”, because they are.
< makes sense because the 2 chains are finite numbers and infinitely big numbers and an infinitely big number is bigger than any finite one because it’s , well, infinite. I can elaborate more technically, but I think trying to develop some numeracy for infinite numbers is a lot like learning about negatives and rationals and complex numbers. Just play with some expressions and get used to them. then look at the more technical treatment even if you have the ability to read it. Someone gave that example with a flat list but I think and feel that tapping into one’s existing NUMBER (and not list) sense is very powerful since it’s the first math we learn and the only one people use every single day.
“This” is the broken duality phenomenon?
Through stone duality. What about them in particular?
Just because 2 things are opposites, doesn’t mean they’re just the same but flipped
thanks, i think. how’d you find the content?
Nature is an infinite sphere whose center is everywhere and circumference is nowhere
I think there’s an implicit element of scale or one offness. For buying milk you have multiple samples as to good price. Even if any is contrived, the bulk still capture something real
reminded me of https://en.wikipedia.org/wiki/Winner%27s_curse
lol laffy taffy is too real banana sucks
Train skill of noticing tension and focus on it. Tends to dissolve. No that’s not so satisfying but it works. Standing desk can help but it’s just not that comfortable for most.
that the functional analysis is mildly helpful for understanding the problem, but the focus of the field doesn’t seem to be on anything helpful. VC dimension is the usual thing to poke fun at, but a lot of the work on regularization is also meh
Dissection tonight at Merritt College in Oakland, building S202. 5:30-9, you can pay by paypal.
UCSF willed body program, on contract to Merritt College.
(Something that came up yesterday, parens give the particular case.)
Have you spent a lot of time on a skill without a cap? (like math)?
Have you paid money for it? (math tutoring)
How much?
How much have you paid towards a complementary unbounded skill (managing people, voice coaching).
So yeah, between learning another hour of math and a voice coach, both at $~80/hour, is the marginal util of voice coach[1] way lower[2]?.
- ^
Or whatever soft skill you would benefit from but don’t do.
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way because estimates of utility are fuzzy. [don’t lie to yourself.](https://www.goodreads.com/quotes/302239-above-all-do-not-lie-to-yourself-a-man-who)
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From Goldblatt, since {0..H} is internal.