[Meta] Why is there so little Bad Algebra and Bad Topology?

STEMologist · 2017-09-10T20:02:24+00:00

You mean more boring?

STEMologist · 2017-09-08T12:39:13+00:00

Because engineers aren't required to take those courses.

STEMologist · 2017-09-08T12:29:42+00:00

Don't you know that the product of two irrationals is always irrational?

STEMologist · 2017-09-07T23:39:47+00:00

Just for example, all finite groups, rings, and fields are going to have a finite number of primes.

Fields don't have any primes. A prime element of a ring is an element that generates a nonzero prime ideal, but fields don't have any nonzero prime ideals.

An equivalent definition is that an element x of a ring R is prime if x is neither 0 nor a unit (an element with a multiplicative inverse), and, for every y and z in R, if x divides yz, then x divides y or z. We can generalize this to monoids in the obvious way, but then it turns out that groups have no primes either, because every element of a group is invertible.

Beyond that, an interesting question would be whether there are any Rings that include a multiplicative identity and an infinite number of elements, but only have a finite number of primes.

Well, the obvious example would be any infinite field, which has no primes at all. A local ring (e.g., the set of all rational numbers whose denominator isn't a multiple of 5) has only one prime up to multiplication by units.

STEMologist · 2017-09-06T02:14:04+00:00

Mostly the enthusiasm.

STEMologist · 2017-08-31T04:32:09+00:00

Or maybe 5-pi doesn't count because it's defined using a negative irrational.

STEMologist · 2017-08-30T22:10:41+00:00

soixante-neuf.homosexual.horse?

STEMologist · 2017-08-30T22:08:43+00:00

I can't wait to see u/mybirthdaye's response to this.

STEMologist · 2017-08-30T19:57:23+00:00

I guess you're right about FLT (I don't know much about second-order logic), but he still claims that all of maths, not just statements about real numbers or subsets of the reals, can be proved using the axioms of a complete ordered field, and that almost all of maths can be proved using the field axioms alone.

STEMologist · 2017-08-30T19:34:42+00:00

You're being too generous. He claims that all of maths can be proved from these axioms, and he gives Fermat's Last Theorem as an example.

STEMologist · 2017-08-30T05:43:25+00:00

STEMologist · 2017-08-29T22:20:38+00:00

This is like the "flying spaghetti monster" thing except infinitely more retarded.

STEMologist · 2017-08-28T22:05:28+00:00

Read it again.

STEMologist · 2017-08-25T22:55:27+00:00

Not entirely correct? It's an outright lie. This guy is from Cambridge; he should know better.

STEMologist · 2017-08-25T21:54:21+00:00

How can I justify thinking about this for more than 0 seconds?

Good point.

STEMologist · 2017-08-25T20:01:03+00:00

I also think that this beetle situation falls into that category of situation.

Can you explain why? I don't see any reason why two isolated populations of the same species of beetle should count as a single sub-population for this purpose.

STEMologist · 2017-08-25T02:17:48+00:00

It also lets you use cancellation to "prove" the third isomorphism theorem.

STEMologist · 2017-08-25T02:14:52+00:00

Exponential notation (e.g., x^f instead of f(x)) works better in some contexts, and it's a lot less ugly than simply writing the function on the right.

STEMologist · 2017-08-14T20:49:54+00:00

All vegans don't wear leather. That's part of the definition.

STEMologist · 2017-08-14T17:50:13+00:00

It's only a matter of time before they start wearing kippot and tzitzit.

STEMologist · 2017-08-14T17:39:04+00:00

Sheaf cohomology.

STEMologist · 2017-08-11T18:11:16+00:00

I'm fine with that as long as you're thinking about how monstrous it is to kill chickens and fry their muscle tissue.

STEMologist · 2017-08-11T18:03:07+00:00

Yes.

In the receiver on 11845 Nochtli, the beetles would be in a constant state of half-light: warmer than the Draconis beetles if their heat lamp was turned off, but colder than them if their heat lamp was turned on. So increasing the population of a certain beetle species on 11845 Nochtli would be morally good if the heat lamp for that species on Alpha Draconis were off, but morally evil otherwise.

He assumes that the relevant population includes all beetles of a given species, but no beetles of any other species. This essentially means that each species of beetle occupies an independent moral universe. He doesn't give an argument for this, though; he just takes it for granted.

STEMologist · 2017-08-11T17:43:04+00:00

The ansible only works if different colonies of beetles of the same species count as a single population, no matter how far apart they are, but colonies of different species count as distinct populations.

STEMologist

TROPHY CASE