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Results tagged with gm.general-mathematics
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user 4600
Questions about mathematics which don't fall into the other arXiv categories. If you have a general question about mathematics but it is not research level, it's off-topic but it might be welcomed on Mathematics Stack Exchange.
14
votes
A set for which it is hard to determine whether or not it is countable.
Here is an example where it is hard in a proof-theoretic sense to determine whether a set is countable.
Jan Reimann and Theodore A. Slaman (in the paper Randomness for continuous measures) study ran …
2
votes
Examples of conjectures whose direct falsity implies different consequences than indirect fa...
Here's an example from computability theory.
Statement $A$:"The Turing degrees are linearly ordered".
Statement $B$: "The $\Sigma^0_1$ Turing degrees are linearly ordered".
Statement $A$ was refut …
- 24.8k
13
votes
Accepted
Example of a function that behaves like another function
This may be more than 15 symbols, but
$$
f(x)= x + \frac{1}{1+(x+\delta-1)^{2n/(2n-1)}}
$$
where $\delta>0$ is small and $n$ is large. For $n=2$ and $\delta=1/10$ it looks like this:
(source)
ED …
- 24.8k
6
votes
What is the term for combining functions $f_1,f_2,\dots,f_n$ into a tuple $(f_1,\dots,f_n)$?
You could call
$$\mathbf r(t)=\langle x(t), y(t), z(t)\rangle$$
the vector function (or vector?) of $(x,y,z)$.
- 24.8k
1
vote
Are there any organized websites for seminar/conference videos?
You can subscribe to tags on Vimeo, and in principle arXiv tags like pr.probability could be used
http://vimeopro.com/staff/tutorials/video/741488
21
votes
Why is the Gaussian so pervasive in mathematics?
(The sort of obvious answer from teaching statistics several times:)
The sum of two independent normal random variables is again normal, i.e., the shape of the distribution is unchanged under addition …
- 24.8k
10
votes
Still Difficult After All These Years
I would like to believe that by 2110 the Langland's program would be reduced to a 10-page pamphlet (with complete proofs) that I could read over breakfast. Is this belief plausible?
In a way, no …