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If all you care about is whether the statement is true, then yes.

But what they're getting at is that we also want to gain an insight of "what is really going on", and it will take time to distill this proof into a theory that gives us a more complete understanding.

You can watch a lot of TV series online on some random pirate sites by simply googling "show x free online". It doesn't even require the relatively simple technical knowledge of using a BitTorrent client.

I now use "ASCII em-dashes" by using two hyphens -- like this. Or--if you prefer no spaces--like this.

I cannot understand what you're trying to say at all.

Ok but no one here actually implied that they think like this.

YouTube already supports that natively these days, although it's kind of hidden (and knowing Google, it might very well randomly disappear one day). Open the description of the video, scroll down and click "show transcript".

In that case, how come they "left in the first days of the job" because "they saw what they were going to work on and peaced out"?

I seriously doubt saying "big blond haired baby who likes burger and fascism" instead of "Trump" would have made a difference for these people.

No, it's both.

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).

What?

This doesn't "need to" exist, it's just a funny parody that someone made.

No, and this is where this formal notion of basis I mentioned unfortunately diverges from what is perhaps more useful in practice.

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.

The set of all real->real functions is still a vector space.

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.

GP's comment was about accepting this actively vs passively, not about being complicit.

Is there any reference to pigs being possessed with spirits that predate the New Testament?

> This might be okay for consumer apps, but maddeningly, the same doctrine gets applied to enterprise applications as well. I've literally heard non-techie employees of a Fortune 100 company ask for their legacy green screen terminals back because the new, flashy SPA was slowing them down.

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.