Viewing profile — redvenom

Good thing I don't care at all what most people care about. If everyone had your attitude we'd all be listening to pop music instead of classical as well.

This highlights the difference between someone who cares about image quality and someone who just cares about reactions and likes.

In most situations that photographers actually care about (i.e. capturing beautiful, good light), ILCs already murder the iPhone. Computational photography may be cool but it is ju…

The iPhone 12 may have some cool auto computational features, but in no way is it better than an ILC camera like a DSLR. If you actually compare image quality side by side, a DSLR …

There's not much difference between the different formats in terms of engineering genius. The Raw data from a camera is basically a matrix of numbers...not too much innovation poss…

Me too. For people on shared hosts (hundreds of small websites including small businesses), PHP is pretty much the only server-side language that you have access to (well, maybe as…

It is a diagram whose vertices are mathematical objects and whose arrows are morphisms (often functions) between those objects such that any two paths between two vertices represen…

I was thinking the title meant that I could sync an iPad with Linux...too bad. I was hoping that someone made it possible to sync music with the latest iOS.

Absolutely true, there is a lot to prove there. It's not an elementary explanation by any means, rather it is an outline that someone who knows Galois theory well could probably re…

The reason basically comes down to the fact that every time you perform a compass and straight-edge construction, you are constructing quadratic extensions of number fields, wherea…

It does make you much better at formulating problems. In fact, from my experience as a mathematician and watching others do math, the vast majority of good problems comes after som…

No, polygons in non-Euclidean space makes sense. Polygons and more generally, geometric simplicial complexes in other spaces is a branch of mathematics all by itself (geometric gro…

The reason is because you want to be able to usefully talk about 'true vertices'. Another way to define a polygon is any convex hull of finitely many points in Euclidean 2-space wi…

Work at a job so I can pursue my creative projects like writing blog posts and making documentaries.

Well, there are documented cases of evolution happening during our lifetimes. But I would say as a mathematical process, pretty likely once you have the basic ingredients. Richard …

I'll tell you something about memorizing phyla, orders, families, genera, and species. If you've never had exposure to any of that, it might seem arbitrary. But now, go out in the …

This explanation is somewhat informal, but I gets the point across: a theory is a set function symbols, relation symbols, and axioms governing them. A model is a specific set with …

People have a fascination with "This sentence is false" because it highlights the need to be precise distinguishing between the language of a logical system and a metalanguage to t…

"True" in this context is a technical definition, not some hand-waving thing. A sentence X being true means every model satisfies X. Provable means logical deduction within the the…

Excellent question. It implies an infinite number of statements. For if T is such an incomplete theory and X is a statement true in some models of T and false in others, then T+X i…

This response is not quite right. "It's only completeness [...]" sentence does not make sense. CH is independent of ZFC, period, as proved by Cohen. Talking about 'semantic level' …

Just want to point out that your answer is essentially incorrect. Godel's completeness theorem has nothing to do with the existence of models. It is about the provability of senten…

The answer you got from lmm and others is wrong (I am a professional mathematician and did research in logic). The completeness theorem says simply: if T is a first-order theory (l…

The point is not to prove that 1+1=2. The point is to construct mathematics (all of mathematics) directly from the axioms using a formal language. The objective of 1+1=2 is not int…

There are two separate statements here: 1. Mathematicians often use relatively powerful systems, like reasoning in ZFC about Peano arithmetic. The consistency and completeness of a…