enedil

The key point here is that you shouldn't be thinking of counting as a process that happens in time. How is infinity (here, omega) defined? We just say that it comes after any other natural number. So how to think about it? You shouldn't tell yourself:

- ok, take number n, it's smaller than omega, so what about n+1, n+2, etc. ?

You should be telling yourself - ok, take number n. It's smaller than omega. Now check any other number m. If this property holds for any given number, then omega is greater than any given number, and thus infinite.

If there's someone exceptional, there are often numerous stipends.

Because it's algorithm and not code.

Repost: https://news.ycombinator.com/item?id=9698870

It was expected that activist groups will say that these two companies are breaking GDPR, it is not so obvious that they will be actually fined (as the requests need to be processed by specific institution and might be found unwarranted).

It's a really old debate.

If I understand correctly what law is, I would say that lawmakers make some laws to express what is moral and what's not (according to them), but not always it's true that our moral standards are completely different from the lawmakers'. If the objective is to be moral, then we should ditch contradicting laws.

So you're proposing distributed radix tree?

That's exactly the point of parent comment.

Fast primality testing is of course important from asymmetric crypto. Without it, we couldn't generate big semiprimes.

No, very far from it

We already have quick algorithms that say "is it prime" with certainty. Reducing the required time from O(log^6(n)) to O(1) isn't particularly important from cryptographic point of view.

https://en.wikipedia.org/wiki/Primality_test#Fast_determinis...

From my POV, he definitely positioned himself as someone that doesn't give a damn about user privacy

Perhaps having legitimate purpose for data collection in the first place helps.

A friend of mine from Lviv tells me that Ukrainian language is closer in structure and vocabulary to Polish than to Russian. I can't really assess this information, as I speak only Polish, from these three.

So is it actually O(n^2)? Because that is a solution that can be implemented.

What distribution are you on?

My latest (!) stable Fedora still points at py2:

    ~ $ ls -als /usr/bin/python
    0 lrwxrwxrwx. 1 root root 7 Mar 14 14:36 /usr/bin/python -> python2*

Yes, I do it too - I have ublock orogin, privacy badger and httpseverywhere. I do it because the web is faster without ads and trackers. Just look at devtools and see how much time is saved by blocking requests.

Whining about Comcast might be actually valid, but for most people of this world it's largely irrelevant. People from every place have Facebook access. Comcast customers are minority - Americans are minority. That's why Facebook has a lot harder time (also, ditching Facebook is more achievable).

The descriptions are utterly useless. Instead of giving short account of capabilities, we're faced with advertisment.

I suspect that computing Fibonacci numbers with Binet formula is slower than with matrix form - if mul(n) is the number of multiplications required to compute x^n, then matrix form will use 8 * mul(n) integer multiplications, while Binet's formula requires 2 * mul(n) floating point operations. I suspect the latter is slower.

Unfortunate, that your results for `n = 90` are completely useless, since F_90 > 2^32 which is the size of int.

Also, you could have shown a method which is O(log n), namely [[F(n+1) F(n)], [F(n) F(n-1)]] equals [[1, 1] [1, 0]] raised to the power of n.

What other library tells you about complexity? And as you tell, if you don't know algorithns well, I'm pretty sure your implementations won't have better complexity.

Look at any computer algebra system, for exaple sympy (https://sympy.org) and see how they implement it (it's open source).

For every rational, there are infinitely many rational numbers too, since finite cartesian product of countable sets is countable.

I frequently use Ctrl-tab or ctrl-shift-tab more than once at a time. It makes sense to preheat tab for a while after first usage of this shortcut.

I wonder why when people are talking about some math discoveries, there's always someone who'll mention that truly marvellous proof by Fermat (or at least his Last Theorem). That has become repetitive and quite often without a link strong enough to justify expressed opinion.

If you write it and it doesn't finish in a minute, I'm sure it's not that trick.

As nice as it is, integers are not a field (i.e. most of them don't have multiplicative inverses, or 1/n usually isn't integral).

Another good writeup: http://andrea.corbellini.name/2015/05/17/elliptic-curve-cryp...

I would rather tell "Shinichi Mochizuki"

Don't be embarassed for paying for open source.