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1500 questions
166
votes
7 answers
Find a real function $f:\mathbb{R}\to\mathbb{R}$ such that $f(f(x)) = -x$?
I've been perusing the internet looking for interesting problems to solve. I found the following problem and have been going at it for the past 30 minutes with no success:
Find a function $f: \mathbb{R} \to \mathbb{R}$ satisfying $f(f(x)) = -x$ for…
Gamma Function
- 5,642
165
votes
1 answer
What is the Picard group of $z^3=y(y^2-x^2)(x-1)$?
I'm actually doing much more with this affine surface than just looking for the Picard group. I have already proved many things about this surface, and have many more things to look at it, but the Picard group continues to elude me.
One of the…
topspin1617
- 1,683
165
votes
15 answers
Monty hall problem extended.
I just learned about the Monty Hall problem and found it quite amazing. So I thought about extending the problem a bit to understand more about it.
In this modification of the Monty Hall Problem, instead of three doors, we have four (or maybe $n$)…
Shaurya Gupta
- 4,339
165
votes
16 answers
Why does factoring eliminate a hole in the limit?
$$\lim _{x\rightarrow 5}\frac{x^2-25}{x-5} = \lim_{x\rightarrow 5} (x+5)$$
I understand that to evaluate a limit that has a zero ("hole") in the denominator we have to factor and cancel terms, and that the original limit is equal to the new and…
Emi Matro
- 5,013
165
votes
3 answers
The square roots of different primes are linearly independent over the field of rationals
I need to find a way of proving that the square roots of a finite set
of different primes are linearly independent over the field of
rationals.
I've tried to solve the problem using elementary algebra
and also using the theory of field…
user8465
- 1,753
165
votes
1 answer
What's the significance of Tate's thesis?
I've just sat through several lectures that proved most of the results in Tate's thesis: the self-duality of the adeles, the construction of "zeta functions" by integration, and the proof of the functional equation. However, while I was able to…
Akhil Mathew
- 31,310
165
votes
22 answers
Examples of mathematical discoveries which were kept as a secret
There could be several personal, social, philosophical and even political reasons to keep a mathematical discovery as a secret.
For example it is completely expected that if some mathematician find a proof of $P=NP$, he is not allowed by the…
user180918
164
votes
20 answers
How to distinguish between walking on a sphere and walking on a torus?
Imagine that you're a flatlander walking in your world. How could you be able to distinguish between your world being a sphere versus a torus? I can't see the difference from this point of view.
If you are interested, this question arose while I was…
Julien__
- 2,455
164
votes
6 answers
What are the numbers before and after the decimal point referred to in mathematics?
Is there an actual term for the numbers that appear before and after the decimal point?
For example:
25.18
I know the 1 is in the tenths position, the 8 is in the hundredths position but I am seeking singular terms which apply to all of the numbers…
Calvin Froedge
- 1,851
164
votes
2 answers
Example of infinite field of characteristic $p\neq 0$
Can you give me an example of infinite field of characteristic $p\neq0$?
Thanks.
Aspirin
- 5,659
164
votes
6 answers
Is infinity an odd or even number?
My 6 year old wants to know if infinity is an odd or even number. His 38 year old father is keen to know too.
Kevin
- 1,641
164
votes
19 answers
Is there another simpler method to solve this elementary school math problem?
I am teaching an elementary student. He has a homework as follows.
There are $16$ students who use either bicycles or tricycles. The total
number of wheels is $38$. Find the number of students using bicycles.
I have $3$ solutions as…
kiss my armpit
- 3,896
164
votes
16 answers
Intuitive explanation of entropy
I have bumped many times into entropy, but it has never been clear for me why we use this formula:
If $X$ is random variable then its entropy is:
$$H(X) = -\displaystyle\sum_{x} p(x)\log p(x).$$
Why are we using this formula? Where did this formula…
jjepsuomi
- 8,619
164
votes
1 answer
How to determine with certainty that a function has no elementary antiderivative?
Given an expression such as $f(x) = x^x$, is it possible to provide a thorough and rigorous proof that there is no function $F(x)$ (expressible in terms of known algebraic and transcendental functions) such that $ \frac{d}{dx}F(x) = f(x)$? In other…
hesson
- 2,074
- 4
- 18
- 19
164
votes
26 answers
Why does the series $\sum_{n=1}^\infty\frac1n$ not converge?
Can someone give a simple explanation as to why the harmonic series
$$\sum_{n=1}^\infty\frac1n=\frac 1 1 + \frac 12 + \frac 13 + \cdots $$
doesn't converge, on the other hand it grows very slowly?
I'd prefer an easily comprehensible explanation…
bryn
- 9,746