Now use the vector that just points along the x axis (either direction) that line doesn't move, it may stretch a bit (it doesn't as the value is 1) or change direction wrt 2, but the space between your two circles, r=2 and r=3 that it goes though is the same line
Can someone please help me understand how to find the horizontal asymptotes of a rational function? I know the degree of the numerator has to be equal to the degree of the denominator OR the degree of the denominator has to be greater than the degree of the numerator but I don't know and cant figure out how to find the actual number(s)?
@Brittany If you want to be somewhat formal about it, let $r$ be an arbitrary real number and calculate $r-f(x)$. Then $r$ is a horizontal asymptote of $f$ if and only if $0$ is a horizontal asymptote of $r-f(x)$.
What are the best methods to accurately generate random integers distributed according to a power law? The probability of getting $k$ ($k=1,2,\ldots$) should be equal to $p_k = k^{-\gamma} / \zeta(\gamma)$ and the method should work well for any $\gamma > 1$.
I can see two naive approaches:
C...
@Brittany You can, in some sense, solve for it. For instance, once you simplify my expression, there will be a unique $r$ such that the numerator is constant.
Then the HA for $f$ will be $r$.
@Brittany For HA not equal to $-1$ try $\frac{x+1}{6x-1}$.
@Brittany There is a recipe for doing this formally somewhat like what I said above, but no one actually does that. You may find this annoying. Instead, we use "trick": namely ignore all terms but the terms of highest degree in the numerator and denominator.
I approved the flag simply because it looked potentially trollish since it was out of the blue and I couldn't see any recent activity from the user in here. I would have dismissed it if it was just random language from a regular
but I went to a high end comp sci school that was all theory, and it was a regular statement from first and second year professors to tell students they were great programmers but not computer scientists
which also probably explains the 65% attrition rate we had in the major
Well there are other kinds of criminals who don't get jokes. For instance, murderers never get jokes because they kill the joke teller before the punchline.
Prove $ (A \cup B) \cap C$ = $(A \cap C) \cup (B \cap C) $
Starting from the left side,
$ (A \cup B) \cap C = $
By distributive law, ( distributing the $\cap C$), we have
$ (A \cap C ) \cup (B \cap C) = $
Therefore,
$ (A \cap C ) \cup (B \cap C) = (A \cap C) \cup (B \cap C)$
If I start ...
@KarlKronenfeld After the author stops talking about the actual problems with a modern war for the JWT he begins to ramble and it's hard to see what his point is
Prove or disprove $(A + B) \cap C = (A \cap C) +(B \cap C)$
I want to disprove this statement.
$(A+B)$ is the symmetric difference and has the form of $(A \cup B) \backslash (A \cap B)$
I am starting on the left which is $(A + B) \cap C $
If I take the complement definition of $(A+B)$, I wou...
@KarlKronenfeld what I got out of the article is that the author thinks there's no further value for the classical theory of JWT, but that a modern one that changes focus might still have untapped value
@Mike I thought that the author was saying: (1) yeah sovereignty is crumbling in the modern times but battles aren't fought among them anyway, (2) the larger blocs like the UN will have to consider the questions implicitly posed by the JWT eventually, (3) the existence of nuclear weapons does not fundamentally change warfare since they are unlikely to be used (we're using other high-tech weapons)
Yeah, you are definitely right in that the author wants to perhaps shift focus, but I disagree about whether the claim is "there is no further value for the classical theory"
I definitely overphrased that - the parts that he objects to most are essentially the requirements of proportionality and sovereignity perhaps need to be re-examined or roughly ignored in favor of the other topics, simply because it's hard to not fail those immediately
And he's not willing to consider war trivially immoral, but rather that if one's going to be making the argument that it is, it should be more subtle
immoral's not the right word, but you get my meaning
What are the best methods to accurately generate random integers distributed according to a power law? The probability of getting $k$ ($k=1,2,\ldots$) should be equal to $p_k = k^{-\gamma} / \zeta(\gamma)$ and the method should work well for any $\gamma > 1$.
I can see two naive approaches:
C...
Prove $ (A \cup B) \cap C$ = $(A \cap C) \cup (B \cap C) $
Starting from the left side,
$ (A \cup B) \cap C = $
By distributive law, ( distributing the $\cap C$), we have
$ (A \cap C ) \cup (B \cap C) = $
Therefore,
$ (A \cap C ) \cup (B \cap C) = (A \cap C) \cup (B \cap C)$
If I start ...
