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May
7
comment Traveling salesman problem: why visit each city only once?
The same section of the Wikipedia article you cite in your last paragraph points out that if you lift the every-city-exactly-once condition, any non-metric TSP can be reduced to a metric TSP by replacing the distance between any pair of cities with the length of the shortest path between them. Then the triangle inequality holds on the modified problem, and Michael's answer applies.
May
6
comment Maximization of a function I came up while studying
What does $\min(\bar y,\theta)$ mean when $\bar y$ is a vector?
May
6
comment Can there be an infinitely long line, that you could get infinitely closer to the end of?
Well, I'd say $2$ is closer to infinity than $1$ is, just as $1$ is closer to zero than $2$ is. So you can get closer and closer to infinity just by increasing the number.
May
6
comment Why is the unit normal of plane curves defined to be rotated?
Now that you've corrected the typo, the confusion is resolved: $\bigl(-y'(t),x'(t)\bigr)$ is clearly not the same as $\bigl(x''(t),y''(t)\bigr)$ rotated by $\pi/2$.
May
6
comment Is a pattern proof?
@timmbob physics.rutgers.edu/~dingding/prime.html
May
5
comment Using axis coordination to represent rotation matrix instead of angles
Just having one vector in both reference frames is not sufficient. For example, knowing where the nose of a plane is pointing does not fix its orientation: it might be performing a roll.
May
3
comment Intuition: “If P then Q” = 'Not P or Q'
That's just more of the "no, this doesn't help" that you've been repeating. Do you have any sense of what would help? What is missing or insufficient in Cameron Buie and Brian M. Scott's answers?
May
3
comment Intuition: “If P then Q” = 'Not P or Q'
So you've seen Cameron Buie and Brian M. Scott's answers, and you even commented that Cameron's answer gave you instructive intuition. Can you explain what you find missing or insufficient in those answers? Given that so many people are putting in the effort to try to help you, it's only fair that you put in the effort to explain what kind of help you need.
May
3
comment Intuition: Why is the biconditional true if both statements are false?
Anyway... Just change the example you like to "If and only if pigs fly, I will give you $1,000,000".
May
3
comment Intuition: Why is the biconditional true if both statements are false?
What's more intuitive than "$P$ and $Q$ have the same truth value"? They must be both true or both false.
May
2
comment Why does the graph of an exponential function shoot straight up when getting to x=1 in an exponential growth function with x^huge number?
Because $1^{\text{huge number}}=1$ but say $1.01^{\text{huge number}}\ge1+0.01\times\text{huge number}$. So if $\text{huge number}>10000$ then already the graph is higher than $100$ for just $x=1.01$.
May
2
comment How to reconstruct a symmetric matrix given the eigenvalues and eigenvectors.
You shouldn't orthogonalize eigenvectors unless they have the same eigenvalue, should you?
May
2
comment Is $(a+bi)(a-bi) = a^2 + b^2 $ solely a real number or a complex number?
$\arg$ is the function that gives the argument of a complex number. So you can say $\arg z_1=\theta_1$, and $z_1=re^{i\theta_1}$, but it is not correct to say $z_1=r_1\arg\theta_1$.
May
1
comment 'is an element of $\emptyset$' vs 'were an element of $\emptyset$'
Since you already know that $\emptyset\subseteq A$, and you are asking rather about how Gowers' instincts work and whether/why the meanings of his statements differ, this seems to be more a question of linguistics and/or psychology than a question of mathematics.
Apr
30
comment Examples of results failing in higher dimensions
On MathOverflow: Results true in a dimension and false for higher dimensions
Apr
30
comment What are some examples of generalizations to higher dimensions which do not hold?
Previously: Examples of results failing in higher dimensions and on MathOverflow: Results true in a dimension and false for higher dimensions
Apr
30
comment algorithm for generating a random non-degenerate matrix over $[0,1 ]$?
Are the entries of $V$ only $0$ and $1$ or any real number in between? If the latter then any random matrix has probability $1$ of being invertible.
Apr
30
comment What are numbers?
I think we've had this question before: What exactly is a number?
Apr
29
comment If a computer can check 1 million colorings per second, about how long would it take to check all possible three-colorings on 100 vertices?
There are $3^{100}$ possible colourings. Divide by 1 million and that's how many seconds. If you don't want to calculate it yourself, ask WolframAlpha (which helpfully also tells you the answer in multiples of the age of the universe).
Apr
29
comment Why is a statement “vacuously true” if the hypothesis is false, or not satisfied?
See In classical logic, why is $(p⇒q)$ True if both $p$ and $q$ are False? and Assumed True until proven False. The Curious Case of the Vacuous Truth