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1d
awarded  Sportsmanship
1d
comment $b^{\frac{m}{n}}=(b^{\frac{1}{n}})^m=(b^m)^{\frac{1}{n}}$ except $b$ is not negative when $n$ is Even.
@SufyanNaeem: I notice that you also edited the quote. That means either the original quote or the current quote is not correct (because there's only one thing that's in the book). In particular, your edit changed the meaning of the quote.
1d
answered Proving $AD_1A^{-1}=D_2$
2d
comment What is the function that generates this graph?
Your function would give e.g. $(4,0)$ instead of $(4,1)$ and $(7,3)$ instead of $(7,7)$.
2d
comment Does color affect purchase decisions across items?
Well, it would be sufficient if you replaced "if all students at his school have an equal opportunity" by "if course assignment is uncorrelated to being on the honour roll."
2d
comment Proving $AD_1A^{-1}=D_2$
Hint: Applying $A$ from the left gives permutation of the rows. Applying $A^T$ from the right gives permutation of the columns. The diagonal consists of all matrix elements where the row index equals the column index.
2d
comment Up to isomorphism
@yons: Yes. Basically it says the labels are effectively just that, names for the group elements; to use a non-group example, up to relabelling isomorphism, the sets $\{1,2,3,\ldots\}$ $\{\text{one}, \text{two}, \text{three}, \ldots\}$ and $\{|,||,|||,\ldots\}$ are the same if the arithmetic structure is defined appropriately.
2d
comment $b^{\frac{m}{n}}=(b^{\frac{1}{n}})^m=(b^m)^{\frac{1}{n}}$ except $b$ is not negative when $n$ is Even.
OK, I've posted it as answer (with a slight extension).
2d
answered $b^{\frac{m}{n}}=(b^{\frac{1}{n}})^m=(b^m)^{\frac{1}{n}}$ except $b$ is not negative when $n$ is Even.
2d
comment Does color affect purchase decisions across items?
Strictly speaking the data given is not sufficient to decide Andrew's believe because there might be other influences that affect both the admittance to the honour roll and the assignment to courses; for example, there may be a preference to give the history class to people who already had history the previous year, and being in the history class may also be seen favourably when considering admittance to the honour roll. In that case, being on the honour role would not get you any advantage, yet you might still see a significant correlation in the history class data.
2d
comment $b^{\frac{m}{n}}=(b^{\frac{1}{n}})^m=(b^m)^{\frac{1}{n}}$ except $b$ is not negative when $n$ is Even.
The quoted sentence says "if the conditions are fulfilled, then the claim holds." That's known as a sufficient condition. It does not say "if the conditions are not fulfilled, then the claim doesn't hold". That would be a necessary condition. Since only the sufficient condition was claimed, the only way to disprove the claim would be to find a case where the conditions are fulfilled but the formula doesn't hold. None of your examples qualify, since they all use $b=-1\notin\{0,1,2,3,\ldots\}$.
2d
comment $b^{\frac{m}{n}}=(b^{\frac{1}{n}})^m=(b^m)^{\frac{1}{n}}$ except $b$ is not negative when $n$ is Even.
I can't find the word "only" in the quoted claim, so it's only given as sufficient condition, not as necessary condition. Thus you haven't disproved the condition in the book; what you have disproved is the (not claimed) assumption that it is a necessary condition.
2d
answered Up to isomorphism
2d
answered $f:[a,b] \to R$ is continuous and $\int_a^b{f(x)g(x)dx}=0$ for every continuous function $g:[a,b]\to R$
2d
reviewed Approve $\sum_{k = 1}^{n} \frac{1}{k^{2}} < 2 - \frac{1}{n}$
2d
comment Proving that $(u+v)×w=u×w+v×w$
What do you know about $\vec a\times\vec b$? I'm sure it's more than "there is an operation $\times$ that takes two vectors and gives a vector" (which wouldn't be sufficient to prove that equation anyway). On the other hand, that equation seems not to be among what you were told about it (or otherwise asking to prove it would be pointless).
2d
comment Convergence: infinite series
So what is your question? How to prove it?
2d
revised Why are we defining the norms on certain vector spaces the way they are?
added 218 characters in body
2d
answered Why are we defining the norms on certain vector spaces the way they are?
2d
revised Prove a sequentially compact metric space is bounded.
fixed math formatting