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13h
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.
14h
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 $(7,7)$.
14h
comment How do I determine if a statistical relationship exists in a real life problem: honor roll class assignments?
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."
14h
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.
14h
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.
14h
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).
14h
comment How do I determine if a statistical relationship exists in a real life problem: honor roll class assignments?
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.
15h
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 $b=-1\notin\{0,1,2,3,\ldots\}$.
15h
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.
1d
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).
1d
comment Convergence: infinite series
So what is your question? How to prove it?
1d
comment Prove $ (A \cup B) \cap C$ = $(A \cap C) \cup (B \cap C) $
That link gives a 404 not found.
Apr
22
comment Zero to the zero power - Is $0^0=1$?
@user21820: Thank you.
Apr
21
comment How to solve the derivative of $b^x$ using the defintion
Thinking about it, for this task probably the best way to define it is as $\lim_{h\to 0}\frac{b^h-1}{h}$ :-)
Apr
21
comment How to solve the derivative of $b^x$ using the defintion
How do you define $\log b$ without knowing $e$?
Apr
21
comment Oil decay at 13%, how long until it is less than 21% of original?
Still an exponential, just with a different base. The instantaneous rate is the derivative.
Apr
21
comment Oil decay at 13%, how long until it is less than 21% of original?
That would be the solution if it were 13% for the full first year (I assume that with (0.87)2 you actually mean $(0.87)^2$). But as stated, 13% is the instantaneous rate, which immediately starts to decrease.
Apr
21
comment Oil decay at 13%, how long until it is less than 21% of original?
It asks at which point in time the oil in the field is less than 21% of the oil that was in the field before starting oil production.
Apr
20
comment R is commutative ring with identity & define $\circ$ on $R$ by for any $a,b \in R$ $a \circ b=a+b-ab$ Prove the following
I think in the last sentence you mean $1=0$ ($1\ne 0$ doesn't follow from $a=a-1$ and is certainly not false in a field).
Apr
20
comment Analog clock with same hands - sometimes one can't tell time
Done (I actually started with it before your latest comment, but due to being detailed, and thinking a lot about the validity of every single step, it took me quite some time).