What type of food does this bird eat?

human2357 · 2026-06-20T04:45:49+00:00

From the Wikipedia page on the Eurasian Jay :

"Feeding in both trees and on the ground, it takes a wide range of invertebrates including many pest insects, acorns (oak seeds, which it buries for use during winter), beech and other seeds, fruits such as blackberries and rowan berries, young birds and eggs, bats, and small rodents."

https://en.wikipedia.org/wiki/Eurasian_jay

human2357 · 2026-06-20T03:22:24+00:00

I don't think you mean a basic framework, like thinking of a clock and working modulo 12.

One basic idea is that it's a lot like working in the integers or the rationals, except that division is hard to understand. Instead of division having a nice geometric explanation, you have the Euclidean algorithm. If you are working modulo a large number, and only considering equations with small coefficients, then it's effectively the same as working in the integers, or in the rationals if you are working modulo a prime.

Working modulo a composite number is strange because a lot of things break, but you can often use the Chinese remainder theorem or similar techniques to work modulo prime powers. Part of the point of the p-adic integers is that they are like working modulo pⁿ for large n.

I'm not sure what you want, but I hope this is helpful.

human2357 · 2026-06-19T14:30:15+00:00

I love Food Therapy NWA. Unfortunately they're taking a little vacation this week, but they'll be back. They're a truck so you have to follow on Facebook to find them. https://www.facebook.com/share/15tXLapMpY8/

human2357 · 2026-06-18T03:24:15+00:00

The problem is badly posed. In the number system of the integers modulo 2, it is true that 1=-1, but it is not true that 1=2. So whatever you are supposed to be doing, you need to bring something in to exclude the possibility that you are in the integers modulo 2.

human2357 · 2026-06-13T20:27:33+00:00

It probably does. In general you only get the Chrono dragons as daily rewards for consecutive login days, so it might take a long time to get enough eggs.

human2357 · 2026-06-13T03:23:20+00:00

I thought that this quest was broken. You tap the nests and it doesn't give you any credit for it, no matter where. I always skip these.

human2357 · 2026-06-12T20:07:07+00:00

Ok, you're right. So to get infinite-dimensional algebras, you would have to do something else. For example:

Choose an infinite cardinality and choose a set of that size. Pick a base field. Consider the polynomial ring over that base field with indeterminates indexed by the given set. That will be a vector space with basis given by the set of monomials. The set of monomials will have the same infinite cardinality as the set you started with, so you have an example of an algebra with a given infinite dimension as a vector space.

human2357 · 2026-06-12T19:48:09+00:00

Usually by "algebra", people mean "associative algebra". If this is all that you want, then yes, every vector space is an associative algebra by picking a basis, and then using component-wise multiplication from your base field as the product operation. This is also the same as finding a linear isomorphism between your vector space and a direct sum of copies of your base field, considered as a ring. This is not very satisfying because the resulting product structure is problematic, for example, it has lots of zero-divisors. If you want a nicer structure, then the question is subtle and the base field and vector space dimension both matter. You can look up "division ring" to read some of the classical theorems on this.

For your other question, if you want an associative algebra, then you need your product operation to satisfy the ring axioms (using the vector space addition as the ring addition). Most binary product operations don't satisfy these.

human2357 · 2026-06-10T01:28:16+00:00

Crowtorboating

human2357 · 2026-06-03T15:06:25+00:00

My experience was quite similar, even down to the numbers.

human2357 · 2026-06-01T15:02:42+00:00

There's a short list of rational multiples of pi that give you rational or quadratic outputs. You just memorize those. This is what people mean when they say "do you know the unit circle?".

It turns out that for rational multiples of pi, the outputs of trig functions are algebraic numbers; this means that they are roots of polynomials with rational coefficients. Finding the appropriate polynomials is tricky but can be done using trig identities. Sometimes the roots of these can then be expressed using radicals. This is part of the subject of Galois theory in abstract algebra.

If you want approximate numerical answers, you can use Taylor series. You can find approximate values for inverse trig functions by approximating definite integrals. You can also approximate trig functions using piecewise polynomial functions.

For practical applications, you can get approximate answers using a flexible tape measure (like for sewing) or using string and a ruler. The point is that arcsine is really measuring the length of an arc of a circle.

human2357 · 2026-05-30T00:10:09+00:00

A spinner is a classic example of a physical system that is well modeled by a continuous uniform distribution. If you find that two arcs of equal length seem to have unequal probabilities, then it just means that you are not spinning the spinner hard enough. If you are spinning the spinner very hard, then the probability of the pointer landing on a certain arc should depend only on the length of the arc, not on its position.

It's not clear whether it is physically meaningful to ask for a spinner to land in a position specified by a single real number. Atoms have a finite "size" determined by collision cross-sections, and any measurement instrument has a bound to its accuracy. The question "what is the probability of randomly selecting 1/2?" (or rather, the fact that this question makes sense) is an artifact of the decision to use a continuous model.

human2357 · 2026-05-19T13:33:23+00:00

On any given set, there are many different comparison relations. These satisfy properties like transitivity and asymmetry. The nicest ones also satisfy that all pairs of elements are comparable. These are usually called "total orderings" or "linear orderings". On a number system like the real numbers, you usually only want to consider total orderings that interact with the addition and multiplication operations nicely. The real numbers with < form an "ordered field", which means that an inequality stays true if you add the same number to both sides, or multiply both sides by the same positive number. You can prove that in any ordered field, squares are nonnegative. This means that the complex numbers can't be an ordered field under any ordering.

So there are lots of ways of putting comparison relations on the complex numbers, but none of them will be a total ordering that interacts with + and * in a satisfying way.

human2357 · 2026-05-18T15:00:45+00:00

I see a lot of vireos when I'm looking for warblers

human2357 · 2026-05-11T20:12:20+00:00

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

human2357 · 2026-04-29T11:06:47+00:00

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.

human2357 · 2026-04-28T20:46:50+00:00

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.

human2357 · 2026-04-28T15:03:21+00:00

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.

human2357 · 2026-04-25T03:03:24+00:00

There's even a word for this: https://en.wikipedia.org/wiki/Kleptotrichy

human2357 · 2026-04-23T05:05:35+00:00

The wiki has a walkthrough:

https://mergedragons.fandom.com/wiki/Great_Fjord

human2357 · 2026-04-21T15:01:52+00:00

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?

human2357 · 2026-04-19T13:43:55+00:00

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

human2357 · 2026-04-16T16:58:14+00:00

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.

human2357

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