Recent content by Prof B

You say that you learned about ranks. Did you learn the following? rank(A) ##\geq## rank(AB)? If A is nxn and rank(A) = n then A is invertible. You could prove that A is invertible using 1 and 2.

For a long time, mathematicians wrote ##A \subset B## to mean "A is a subset of B". It's easier to write than the other one. "Proper subset" arises so rarely that it can be written out in words when needed. As such, it has never needed its own symbol. With the advent of computer typesetting...

It is good that you are interested in this sort of thing. Note that in the case that X is between A and B it is not necessary to calculate |AX| or |BX|. That sort of observation is helpful when you try to work out other cases yourself.

I can't tell from your picture, but assume that the leftmost point in the triangle is A and the rightmost point is C. The line segment that you labeled h is not an altitude in ABC. Draw the line containing BC. Draw a line through A perpendicular to the line containing BC. Say it intersects...

Two parts of the question are worded strangely: "Paul and Allen take the card" "there are certain cards for Allen to take, but not for Paul" I wonder if the question was translated incorrectly. As I understand the game, Paul can take 34 cards.

No conclusion about n is drawn in Case 2. Since you are not doing a proof by cases, you really shouldn't write "Case 1" and "Case 2".

Inscribed means that all corners are on the surface. That's why g=1.

3 equal numbers add up to 1. Are you really questioning how he deduced that each number is 1/3?

This is a physics forum. I learned to use units from a physics teacher. My math is better because of it.

I found a python program on stackexchange that uses dynamic programming to calculate the probability that no consecutive cards have the same suit. It could be modified to handle ranks instead of suits, but I found a really impressive solution for ranks on AskMeta. You have to scroll past a few...

I found the answer here. Can anyone explain it?

If you differentiate with respect to p then you don't have to write p' at all and you don't get the spurious solution p'=0, so it's easier. It's like differentiating a polynomial.

Multiply out the right side before taking the derivative. It will be easier.

There is a general method to safely change order of integration or summation. First write all of the ranges as inequalities, i.e., $$ a \leq x \leq y $$ $$ a \leq y \leq z $$ $$ a \leq z \leq b $$ Combine them into a single chain of inequalities, i.e., $$ a \leq x \leq y \leq z \leq b $$ Break...

I don't think the problem is very well stated. What is c? Is ## I_k ## really the 3rd unit vector for every k; that would make ## g(I_1, ..., I_n) = 0 ##. Also, please write ## , \ldots, ## instead of ## \cdots ## unless you really mean iterated multiplication.