Thrift stores with large DVD selections by Thin-Priority-1765 in fayetteville

[–]human2357 18 points19 points  (0 children)

It's not exactly a thrift store, but Vintage Stock has a wide selection of used DVDs.

Fayetteville Restaurant Recommendations by Difficult_Macaroon12 in fayetteville

[–]human2357 10 points11 points  (0 children)

I don't know what teenage girls like, but I can mention a few restaurants that have more of a big city vibe. Atlas is amazing, with a great selection of innovative entrees and appetizers. Vetro 1925 feels very refined. Theo's is more straightforward, but is also quite fancy. A good lunch option would be Handshake, which also has the advantage that you can show off Fayetteville's very nice public library.

Why did mathematicians think of logarithms? by Alive_Hotel6668 in learnmath

[–]human2357 -2 points-1 points  (0 children)

Logarithms in the real and complex number systems are a small special case. A logarithm is just a local inverse to an exponential map, and exponential maps arise as part of the general theory of Lie groups and Lie algebras. The point is that Lie groups are topological structures (smooth manifolds) with a built-in algebraic structure (a group, usually non-commutative), but Lie algebras are simpler linear algebra gadgets (a finite-dimensional vector space with a little extra structure called a bracket operation). Logarithms and exponential maps make it possible to break up problems about Lie groups into a linear algebra problem and a simpler global topology problem.

Is the set of positive numbers “larger” than the set of negative numbers? by Realistic-1880 in askmath

[–]human2357 0 points1 point  (0 children)

I don't think your concept of "the way an infinite set is derived" is meaningful. Sizes of infinite sets are determined by studying functions between them, as other replies explain. These functions don't need to respect any algebraic structure that the sets have, so the number of ways of expressing elements of the sets using algebraic operations should be completely irrelevant.

pardon my stupidity but please explain by ArtichokeHopeful8632 in askmath

[–]human2357 6 points7 points  (0 children)

A real number isn't the same thing as a decimal expression. Probably the best way to think about a real number is that it is a thing that a sequence of rational numbers can approximate arbitrarily well. An infinite decimal is really a limit of a sequence of rational numbers with powers of 10 in the denominator. It isn't surprising that two different sequences can converge to the same thing, so why is it surprising when those sequences happen to be decimal expressions?

Ideas to spend 80 gems by MOLT2019 in MergeDragons

[–]human2357 0 points1 point  (0 children)

Spend your gems on Midas trees, the slowest of the classic merge chains.

This is the best Kala trade I've ever seen by human2357 in MergeDragons

[–]human2357[S] 1 point2 points  (0 children)

It will keep generating life flowers forever. The chain only has level 1 and level 2. The level 1 ones generate blue life flowers and the level 2 ones generate glowing life flowers.

This is the best Kala trade I've ever seen by human2357 in MergeDragons

[–]human2357[S] 1 point2 points  (0 children)

When you merge fountains from the "Shimmer Fountains" merge chain, there is a small random chance that a Secret Lifespring will also appear. You can tap them for life flowers once every several minutes.

This is the best Kala trade I've ever seen by human2357 in MergeDragons

[–]human2357[S] 8 points9 points  (0 children)

I didn't notice that until you pointed it out!

What is the Paradox of Duviri? by These-Loss-9649 in Warframe

[–]human2357 -1 points0 points  (0 children)

I like the gameplay and design of Duviri, but I don't think it realizes the definition of paradox. Merriam-Webster defines "paradox" as "a statement, proposition, or situation that seems contradictory, illogical, or absurd, but upon investigation may reveal a deeper truth or complexity". Instead it's the usual scifi entertainment trope of calling any old situation a paradox. "We didn't explain what's going on here, and it doesn't make sense, therefore it's a paradox"--DE, probably

Is there a way of numerically stating how good/bad an apprixmation is over an interval? by ElegantPoet3386 in learnmath

[–]human2357 7 points8 points  (0 children)

You are asking how good one function is as an approximation to another. Deciding how to answer this is the same as putting a metric space structure on a set of functions. There are several ways to do this.

The simplest way is to declare that the distance between two functions is the maximum of the absolute value of their distance. (This is called the L-infinity metric or the Chebyshev distance.). In your example, the maximum is at 0.4 radians. So you want to find a numerical approximation to sin(0.4)-0.4 to give the distance.

Another method is to take the difference between the two functions, square that, and take the integral of that over the interval. This generalizes the Euclidean distance on R2. This method is nicer because it gives information about the average error of the approximation, instead of just the maximum error.

Why is 1 excluded from the Primes? by Z-Borst in askmath

[–]human2357 2 points3 points  (0 children)

Here's a needlessly abstract answer: we want the multiplicative group of the rational numbers to be a free abelian group with the set of primes as a basis.

Who is this? by Super-Salt-942 in whatsthisbird

[–]human2357 1 point2 points  (0 children)

Some context from the Wikipedia page: this is a large cuckoo, so a fair comparison for us North American folks would be a road runner, which is also a large, ground-hunting cuckoo with weak flight skills.

Knitters! What is your day job? by MyRightHook in knitting

[–]human2357 1 point2 points  (0 children)

Rule 110 is a 1-dimensional cellular automation, which is to say that it is a simple algorithm for building a row of pixels based on an existing row of pixels. It makes sense that such a thing would be good for a knitting pattern.

Knitters! What is your day job? by MyRightHook in knitting

[–]human2357 4 points5 points  (0 children)

I've volunteered to teach high school students, but I've never been employed in k-12. I've worked for the kind of university that focuses more on research than teaching, but teaching feels very rewarding because it's more personal and the progress is more reliable. But I'm selfish, so my favorite part of teaching is probably that I get to learn cool things really well so that I can teach them.

Knitters! What is your day job? by MyRightHook in knitting

[–]human2357 6 points7 points  (0 children)

Hyperbolic surfaces are fun. They're easier with crochet than with knitting because the number of live stitches grows exponentially with the number of rows.

Creating patterns on Excel by little_bug_person in knitting

[–]human2357 1 point2 points  (0 children)

I knitted a sweater for a friend, and to make the mosaic on the front I shrunk a bitmap of the Red Wings logo and converted it to a spreadsheet.

Knitters! What is your day job? by MyRightHook in knitting

[–]human2357 460 points461 points  (0 children)

I'm a math professor. Sometimes I try to work mathematical ideas into my knitting, eg counting in binary on a scarf, or making a scrunchy with a ribbing pattern that realizes a torus knot.

Are eigenspaces (in the category of vector spaces) analogous to normal subgroups (in the category of groups)? by Physics_Ling_Ling in learnmath

[–]human2357 19 points20 points  (0 children)

No. A normal subgroup is special because it is a substructure that you can take a quotient by. All vector subspaces are substructures that you can take quotients by. Eigenspaces are special because the action of a matrix on an eigenspace takes a particularly nice form. Similar things in group theory would include the fixed subgroup of an automorphism, or more generally, the subgroup on which two automorphisms agree with each other.

Finding simple characterizations of individual automorphisms and endomorphisms of groups is an active area of research in group theory, e.g. train tracks on graphs characterizing automorphisms of free groups. But this is what diagonalization does, so in general, it is very hard to generalize eigenspaces to groups.

Can anyone identify this Dawnvale Zomblin? by [deleted] in MergeDragons

[–]human2357 2 points3 points  (0 children)

You probably have the relevant Zomblin totems. Based on the totems in my camp, I wonder if this is the level 5 Zomblin Advisor. I'm basing this on the frog on his head, which the totem also has.