Chinjut

57 ms·

571.
by Chinjut 10y ago
Sure, Markov's principle matters for some things, but it seems to me Markov's principle doesn't really matter for this particular claim ("for every prime p, such-and-such a decidable property phi(p) is true"), since
572.
by Chinjut 10y ago
Sure, but any classical proof of the theorem would automatically yield an intuitionistic (i.e., standard type-theory) proof as well; just run it through the double-negation translation, and then eliminate double-negations using the decidabi
573.
by Chinjut 10y ago
An impressively terse presentation, but that makes it not particularly clear or likely to spark further understanding in someone who doesn't already understand the phenomenon intuitively. Here's the approach I prefer for clarity a
574.
by Chinjut 10y ago
Every proof of this theorem, by any reasoning, would be constructive by the same criteria. You can always do an exhaustive search to determine whether p is a sum of two squares. (Of course, it's not obvious when solutions exist and wh
575.
by Chinjut 10y ago
In response to many of the comments here: There is a frequent pattern which concerns me of primarily justifying the desire for reduced work hours in terms of the alleged increase in productivity this will bring about (by allowing recharging
576.
by Chinjut 10y ago
Sorry, you are wrong. Your description of ${CLASS}-hard is precisely backwards. For example, see Wikipedia: https://en.wikipedia.org/wiki/NP-hardness "NP" itself already means "No harder than NP-complete
577.
by Chinjut 10y ago
Incidentally, sure, we could just pick ^ to be our basic operator and define everything else in terms of that. Well, just as well, we could define everything in terms of logarithm. Or everything in terms of roots! In fact, one might ask why
578.
by Chinjut 10y ago
Why think of ternary relations? Well, if you do not recognize that there is an "Any two variables here determine the third" structure here, you are missing a fruitful insight into the matter. That's why. Sometimes that's
579.
by Chinjut 10y ago
I didn't mean to come across as unduly harsh. But, yeah, I think a misleadingly symmetric looking notation for an asymmetric operation can be a source of confusion (this is also a potential problem with the misleadingly symmetric looki
580.
by Chinjut 10y ago
"And let log base n of x be written as (x v n) or possibly (x \/ n)." "Lots of familiar relationships carry over, e.g. Note that ((x * n) / n) = x. Similarly ((x ^ n) v n) = x." You must mean ((x^n) v x) = n. N
581.
by Chinjut 10y ago
"It introduces three concepts (exponentiation, logarithms and roots) as though they were entirely separate." Hm? This is the exact opposite of what the notation is intended to do. It is intended to emphasize that there is just one
582.
by Chinjut 10y ago
Huh? I'm having a little bit of difficulty following you. The triangle just captures that there are three quantities involved (with any two determining the third). I don't know what you mean with references to bifurcations and bin
583.
by Chinjut 10y ago
Yup. Frequently, in mathematics, we have some ternary relation r(a, b, c) such that fixing values for any two arguments uniquely determines a corresponding value for the third. This encapsulates not only the relationship between a^b = c, lo
584.
by Chinjut 10y ago
You've described a very short algorithm for finding a very long proof. But what the algorithm finds is indeed a very long proof, not a short one, and the reason I say that is because the short algorithm description you gave doesn'
585.
by Chinjut 10y ago
I defined it in the relevant way in the post you're responding to (indeed, inbetween the very words "prime" and "cardinal" where I first invoke the concept): the relevant notion is of a cardinal which can't be
586.
by Chinjut 10y ago
Bezout’s theorem fails in that ring. The particular proof given of Bezout's theorem here uses the fact that modding out the ambient ring by one of its prime (in the sense of not further factorable) elements yields a resulting ring with
587.
by Chinjut 10y ago
This is a good concern. FWIW, though, there ARE natural summability methods which turn mere indexed sequences of terms into sums, without any particular choice as to how to interpret those sequences as specializations of formal series, whic
588.
by Chinjut 10y ago
[Continuation of original comment] We can look at it this way: We can try to assign values to a non-absolutely convergent series by bringing its terms in at less than full strength, producing an absolutely convergent series, and then increa
589.
by Chinjut 10y ago
I didn't think the Numberphile video on this was well done, in its "Math is a bunch of inscrutable magic you laypeople will never understand, and every attempt you (as represented by our camera man) make to voice your dumb intuiti
590.
Millennials will work forever–but they may be happier for it(qz.com)
1 points by Chinjut 10y ago|0 comments
591.
by Chinjut 10y ago
If they're unremarkable, perhaps not...
592.
by Chinjut 10y ago
I suppose it depends on how you define a "city area", but there are a great many with more than the NYC area's mere 20 million people. For example, Shanghai, Karachi, and Beijing each exceed that within city limits alone! (
593.
Top White House Economist Dismisses the Idea of a Universal Basic Income(blogs.wsj.com)
93 points by Chinjut 10y ago|180 comments
594.
by Chinjut 10y ago
It was mentioned in the article: "H. pylori, the bacteria that can cause stomach cancer"
595.
by Chinjut 10y ago
From the article: "Until the late 1930s, stomach cancer was the No. 1 cause of cancer deaths in the United States. Now just 1.8 percent of American cancer deaths are the result of it. No one really knows why the disease has faded — per
596.
by Chinjut 10y ago
> when you hear hoofbeats, think horses Ok. I think the works authored under the name "Shakespeare" were indeed written by Shakespeare.
597.
by Chinjut 10y ago
I mean a cite that Feynman made that joke; where can I find that?
598.
by Chinjut 10y ago
As for whether "the physical model of P != NP is definitionally trivial", I suppose it depends on what "the physical model" is, but I don't see any physical reason why it should trivially be impossible to decide the
599.
by Chinjut 10y ago
I didn't malign others, either, as I didn't call anyone a moron... Yes, it's true I implied that you might think that others who puzzled over P vs. NP were morons. I was, after all, laboring under the belief that you thought
600.
by Chinjut 10y ago
It seems to Feynman's argument works via the opposite of ruling out coincidences of that sort. It shows "If nothing surprising happens, then we expect very nearly zero counterexamples to Fermat's Last Theorem"... But the

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