pmiller2

45 ms·

481.
by pmiller2 6y ago
It's not fear. It's disgust.
482.
by pmiller2 6y ago
Ah, yes, right. Smoothness alone doesn't do it. Nonetheless, I still maintain that the property holds for all functions that we actually care about when doing analysis of algorithms. In particular, it certainly holds for sums and pr
483.
by pmiller2 6y ago
Sure, a subset may struggle. That's beside the point. I'm most interested in giving people who, as I mentioned, have a basic fluency with functions of the real numbers the answer to why you drop constant multiples and everything
484.
by pmiller2 6y ago
Sure it does, for all functions f and g that we actually care about in the CS context for big-O. Hint: what if f and g are smooth?
485.
by pmiller2 6y ago
Cool. Sounds like you're in grad school right now, yeah? I know differential geometry is not exactly the same as differential topology, but I remember taking differential topology in grad school. I was always amused that we never act
486.
by pmiller2 6y ago
One easy way to show that more generally is that if f and g are differentiable, f(x) dominates g(x) iff f'(x) dominates g'(x), by L'Hopital's rule. Details left as an exercise for the reader.
487.
by pmiller2 6y ago
Excellent! The level I was shooting for with my brief explanation was that someone who understood limits at a calc 1 level should be able to get it with a little thinking. I do wonder, though: did you know those things before you read my c
488.
by pmiller2 6y ago
It's a little more than that. You need to account for the fact that n log n dominates n, but not n^2, as well. That's not hard, but you should spell it out. This discussion is making me think that a good way to write a "Big
489.
by pmiller2 6y ago
Ok? I never said anything about PhDs. What I said was that people typically aren't hired in at the associate level. Those that are would typically be professors who have tenure at another institution, meaning that they're alre
490.
by pmiller2 6y ago
Sure, but if you're not on the spot in an interview, the master theorem is simple enough to apply: https://en.wikipedia.org/wiki/Master_theorem_(analysis_of_al...
491.
by pmiller2 6y ago
Of course "hard" is relative. Because I was writing a HN post and not a "Big-O explainer," I didn't provide you with any of that prerequisite knowledge. But, the amount of prerequisite knowledge one needs to under
492.
by pmiller2 6y ago
Every one of these "Big-O explainers" says pretty much the same thing: count (or bound) the number of steps, then take the most significant term, and drop the constant associated with it. None of them explain why you take the m
493.
by pmiller2 6y ago
Then you get to have fun solving a recurrence relation. :-)
494.
by pmiller2 6y ago
It's even worse than that. Because integers a and b are congruent modulo n iff n | a - b, and 1 divides every integer, the integers modulo 1 has only 1 element. This gives you the somewhat pathological object called the zero ring: h
495.
by pmiller2 6y ago
Apparently, someone, or a few someones, downvoted the question before it got upvoted a bunch.
496.
by pmiller2 6y ago
I don’t understand. Are you saying people are claiming she made the whole thing up and was just going around saying she was an associate professor at Harvard?
497.
by pmiller2 6y ago
Not really. Unique factorization is defined up to units, so, factors of +-1 don't matter. 1 is not a prime because it's a unit, and the ideal it generates is trivial; it's the entire ring, so, for Z, it's all of Z.
498.
by pmiller2 6y ago
Huh, I'd never heard of that one. I suppose that means that E8 is the equivalent for octonions? That loses the concept of "prime," which is no surprise, because the octonions are not a field, but I wonder if one could bring
499.
by pmiller2 6y ago
I agree on all counts. But, the other answers that say that p is prime iff p is not a unit, and p | ab implies p | a or p | b, or, alternatively and equivalently, p is prime iff p generates a prime ideal, are really the essential qualitie
500.
by pmiller2 6y ago
That's not a half bad idea if the setup is any more complicated than "clone these repos and run the setup scripts."
501.
by pmiller2 6y ago
Not to mention that universities typically don't hire people at the associate professor level. The first rank is called "assistant professor," followed by "associate professor," and then "full professor."
502.
by pmiller2 6y ago
If you like that, then you'll love this: https://en.wikipedia.org/wiki/Ulam_spiral
503.
by pmiller2 6y ago
You're welcome. ;)
504.
by pmiller2 6y ago
This was my thought as well. It sounds like a 24 hour DHCP lease expiring.
505.
by pmiller2 6y ago
Yes, there is such a thing as complex prime numbers. If you restrict yourself to looking at numbers whose real and imaginary parts are both integers, then you have a ring called the Gaussian integers. A Gaussian integer a + bi is prime if
506.
by pmiller2 6y ago
Indeed, crazy dev setup is definitely like a code smell. I remember at one place, it took me 3 weeks to get to the point where I could merge my first PR. Another place I was at, they handed me a laptop that was already set up to run the c
507.
by pmiller2 6y ago
In theory, maybe. In practice, you'll probably be limited to about 15ms round trip.
508.
by pmiller2 6y ago
Right. I am saying that if the light from my TV reaches me essentially instantaneously, and the audio is on a 10ms delay, that messes with my brain.
509.
by pmiller2 6y ago
If you don't have a conductor, always, always, always follow the soloist or concert master, which ever one you have.
510.
by pmiller2 6y ago
This is correct. The reason is more or less that humans are really, really good at staying in sync, but, even with only 2 parts to listen to, it starts to get almost impossible levels of effort to keep proper time. In person, without any

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