But your comment it missing the point. Parent commenter said it needs to start recording audio and video earlier, and a combination of other circumstances cause the device to send the data. Nobody argues this is acceptable.
Oh really? And do you have built-in microblogging platform? Do you have OCR with English-Chinese and Chinese-English translation? Do you have mobile payments? Do you have discover people feature (by location)? Can you identify movies by recording audio? Not only payments are possible, you can send money to anyone in WeChat. Sadly, some of these functionality are not available for non Chinese people (people without account in Chinese bank).
Omg, you're not thinking he's done all this by hand, right? People here can code such simple things. And you don't need no specific symbols, just arrays of ints (or any suitable type).
If a hypothesis is widely expected-to-be-true, then there needs to be a good evidence towards it, which in turn means that it stood unresolved for a long time. That's why probably most of them are still unsolved.
So in this case you're sure that this is the right abstraction. Here's one that I find equally well fitted: you basically want a stable sort on the list with key function f(x) = 1 - (x % 2)
This is also a standard problem. Do you think this abstraction is worse? If so, why and how?
Notice that mathematicians don't take real numbers for granted too - we need to assume their existence first. Looking at this, complex numbers stop being that arbitrary, just another extension of reals.
Also, it's nitpicking, but i is imaginary, not irrational.
Also, complex numbers were accepted by mathematicians before negative numbers (it's something that boggles minds of some people).
Yes, you can. Order is just a relation, i.e. a set that contains pairs of elements. So for example, let X be the relation <. X is a subset of NxN, the cartesian product of N. We say that n<m if the pair (n,m) is in X. Moreover, we say that (n,n+1) is in X, and whenever (n,m) in X and (m,k) in X, then (n,k) in X. This constitues order on naturals.
Answer to your question number 3 is: well, if I have just one apple, with label 3.1415926535 then obviously it will fit. Notice that no two apples have the same labels.
Now you're conflating two different notions. You're (and your quotes) are talking about the first bullet point from the article. In turn, when taking about the last one, the one chosen by article author, from my experience, I'd say that it's beneficial not to even consider it in time, i.e. don't think about it as process, don't think of it as something completed. There's no completion, since there was no process to begin with. The object just is, and we can manipulate it according to the rules.