195 karma · joined September 16, 2022
The purpose of high school is to give you a wide foundation on everything.
The purpose of an undergraduate degree (in math) is to give you a wide foundation (in math).
In a (math) PhD, you are generally hyper-specialized in a very, very narrow area (of math).
This doesn't "need to" exist, it's just a funny parody that someone made.
You can represent any function f: [-pi, pi] -> R as an infinite sum
f(x) = sum_(k = 0 to infinity) (a_k sin(kx) + b_k cos(kx))
for some coefficients a_k and b_k as long as f is sufficiently nice (I don't remember the exact condition, sorry).This is very useful, but the functions sin(x), sin(2x), ... , cos(x), cos(2x), ... don't constitute a basis in the formal sense I mentioned above as you need an infinite sum to represent most functions. It is still often called a basis though.
This vector space also has a basis (even if it is not as useful): there is a (uncountably infinite) subset of real->real functions such that every function can be expressed as a linear combination of a finite number of these basis functions, in exactly one way.
There isn't a clean way to write down this basis, though, as you need to use Zorn's lemma or equivalent to construct it.
Applying general design principles without taking actual use cases into account is the worst.
A common one is putting heaps of whitespace around each cells in a table. Visually appealing, sure. But unusable if I need to look at more than 8 rows at the same time.
But I understand what you mean. The problem is that 99% of online discussions about politics are not about how it relates to anything else. They are usually the same 5 conversations rehashed over and over again. And for some reason, they are aggressively derailed in that direction.
To my ears [ħ] sounds closer to [x] and [χ] than to [h] (even though the place of articulation is closer to [h]), but I'm sure it's different for people who (natively) speak a language with all three.
Ok, I was mistaken about everything being an Element fork.
To move the goalposts slightly though --- do any of these apps properly support threads (i.e. messages in threads show up in and only in separate views)?
Also, as far as I can tell, there is no real diversity in clients even though Matrix is in principle an open protocol. Everything is either Element or a fork of it, or at least is built on matrix-react-sdk, which makes them all effectively the same.
The kid is 17.
[0] https://byorgey.wordpress.com/2009/01/12/abstraction-intuiti...
However, I still agree with the GP that if you are not on the Play Store, you lose most of your installations.
If someone has already discovered your app and can't find it on the Play Store, they are more likely to assume that it's not supported on their phone, unavailable in their region or whatever. Even if you explicitly tell them to just download the APK, most people will not do that. Keep in mind that the average user probably doesn't even know that you can install apps from outside the Play Store. Or even if they guess that it's probably possible, they might well perceive it as complicated and sketchy.
They may have had other heuristics too that led to inconsistent behavior between users. So it should not be so surprising if some people report that that happened even though it didn't happen to others.
GP's point, as I understand it, is that it is not actually possible to choose a number from [0, 1] uniformly at random in "real life".
I think you could argue that, e.g. in the dartboard thought experiment, the probability of choosing individual points doesn't really matter: only probabilities of measurable subsets with positive measure matter.