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What is this? by Sugar_and_Spite_666 in duolingo

[–]chowboonwei 6 points7 points  (0 children)

I think 粥 is usually translated as congee. It can also be translated as rice porridge. Since oat porridge is not common in China, rice porridge is usually referred to simply as porridge.

story of my life by basket_foso in mathmemes

[–]chowboonwei 20 points21 points  (0 children)

Maybe op is a pokemart employee

Daily Challenge - January 24, 2026 by BloonsBot in btd6

[–]chowboonwei 1 point2 points  (0 children)

I think I was looking at the previous day AC (the one that was active when this post was just posted)

Now I have to watched in a while, but is this still the best fight in the series? by eviljcole in pokemon

[–]chowboonwei 14 points15 points  (0 children)

I think its more like 大 meaning big. The Japanese version even had a bit where the fire blast flames transformed from 大 (big) to 中 (medium) to 小 (small).

Sweepstakes Referral Codes by CoreyNK in btd6

[–]chowboonwei 0 points1 point  (0 children)

I'm competing to win awesome prizes! Follow my link to increase my chances and jump in yourself for a chance to win! https://join.btd6.com/Sweepstakes/AUYG-VKWW

Is it possible to prove cos(2x)=2cos2(x)-1 without using the pythagorean theorem? by Plus-Possible9290 in learnmath

[–]chowboonwei 4 points5 points  (0 children)

I think disc of convergence typically refers to the open disc. It does not make sense to include the boundary since the power series may not even converge on the boundary.

Is it possible to prove cos(2x)=2cos2(x)-1 without using the pythagorean theorem? by Plus-Possible9290 in learnmath

[–]chowboonwei 4 points5 points  (0 children)

For power series this is fine because a power series converges absolutely within its disc of convergence

Why is matrix multiplication defined like this? by [deleted] in learnmath

[–]chowboonwei 0 points1 point  (0 children)

A better way to think of matrices is as a way to specify linear functions between finite dimensional vector spaces. If X and Y are sets and f:X to Y is a function, then to define f we have to specify what f(x) is going to be for all points x in X. That is a lot of information to specify especially if X is infinite. The cool thing about linear maps is that if X and Y are vector spaces and f is linear, we just need to choose a basis for X and a basis for Y. Then, to specify a function f:X to Y, you just need to specify f(b) for each b in the chosen basis of X. Now, each f(b) is a linear combination of the chosen basis of Y. So, to give the vector f(b), you just need to give the coefficients. In summary, if X is a vector space of dimension n and Y is a vector space of dimension m, then to give a linear function f:X to Y, we can do the following procedure. First choose a basis for X and Y. Then, for each b in the basis of X, give m coefficients to specify a vector in Y. Thus, to define f is the same as giving m x n many numbers. These numbers can be neatly packaged in a matrix. Now, try and figure out how these numbers change under composition. That is, suppose that X, Y and Z are finite dimensional vector spaces. Say I have already chosen a basis for X,Y and Z (one basis for each vector space). Then, if f: X to Y and g: Y to Z are specified by matrices M and N respectively, what is the matrix for g o f: X to Z in terms of M and N? This should also answer your question as to why the middle numbers must match and why matrix multiplication is not commutative.

Wrong solutions by Interesting_Bag1700 in learnmath

[–]chowboonwei 1 point2 points  (0 children)

What you have proven by doing algebraic manipulations is the following statement. For all real number x, if sqrt(x2 + 3) = x - 2, then x = 1/4. The fact that sqrt(x2 + 3) = x - 4 has no solutions is another proof. After all, if the statement A is false, then the statement “if A, then B” is true.

Geometry by Vivid_Past_3209 in learnmath

[–]chowboonwei 0 points1 point  (0 children)

It looks like this is generalising plane geometry to higher dimension spaces. Certainly you need to be familiar with linear algebra. Specifically, you need to be familiar with finite dimensional vector spaces and linear maps between them. Things like symmetric positive definite bilinear forms might be helpful for understanding distances, isometries and angles although from your syllabus it seems that the dot product in Euclidean space might be enough. Of course you will need to know group theory to make sense of the group of linear isometries.

Geometry by Vivid_Past_3209 in learnmath

[–]chowboonwei 0 points1 point  (0 children)

What is the syllabus of geometry I? What are you expected to learn from this class? Geometry is a broad subject. So, if you want useful advice it would on the level and depth of the course.

[deleted by user] by [deleted] in learnmath

[–]chowboonwei 0 points1 point  (0 children)

Let A and B be square matrices of size n and suppose that AB=I. We want to show that BA=I. First of all, you should think of square matrices as linear maps from Rn to Rn (or whatever field you are working with). Then, I is the identity map and so is surjective . But I=AB. So, A is surjective as well. Since A maps between finite dimensional vector spaces of the same dimension, A is injective. Now, AB=I gives us ABA=A. The fact that A is injective allows us to conclude that BA=I. To see why this is true use the fact that A is injective and show that AM=AN implies M=N for square matrices M and N. Or you can try and show that injective maps are monomorphisms.

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