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1500 questions
100
votes
12 answers
Why do bell curves appear everywhere?
Why do most probability graphs show a bell curve? I've been wondering why... Is it just something natural, like the fibonacci sequence?
Shreyas Shridharan
- 1,171
100
votes
11 answers
Does notation ever become "easier"?
I'm in my first semester of college going for a math major and it's pretty great. I'm doing well, however, there seems to be huge gap between how difficult /complex an idea is and how convoluted it is presented.
Let me make an example: In Analysis…
Jonathan
- 3,032
100
votes
7 answers
Show that the set of all finite subsets of $\mathbb{N}$ is countable.
Show that the set of all finite subsets of $\mathbb{N}$ is countable.
I'm not sure how to do this problem. I keep trying to think of an explicit formula for 1-1 correspondence like adding all the elements in each subset and sending that sum to…
user39794
100
votes
15 answers
Example of a very simple math statement in old literature which is (verbatim) a pain to understand
As you know, before symbolic notations were introduced and adopted by the mathematical community, even simple statements were written in a very complicated manner because the writer had (nearly) only words to describe an equation or a result.
What…
Cauchy
- 4,019
100
votes
10 answers
Explain "homotopy" to me
I have been struggling with general topology and now, algebraic topology is simply murder. Some people seem to get on alright, but I am not one of them unfortunately.
Please, the answer I need is ideally something very elaborate and extensive,…
John Trail
- 3,279
100
votes
13 answers
Can I think of Algebra like this?
This year in Algebra we first got introduced to the concept of equations with variables. Our teacher is doing a great job of teaching us how to do them, except for one thing:
He isn't telling us what we are actually doing when simplifying/solving…
Nico A
- 4,934
- 4
- 23
- 49
100
votes
39 answers
Unusual mathematical terms
From time to time, I come across some unusual mathematical terms. I know something about strange attractors. I also know what Witch of Agnesi is. However, what prompted me to write this question is that I was really perplexed when I read the other…
VividD
- 15,966
100
votes
14 answers
How to find a general sum formula for the series: 5+55+555+5555+.....?
I have a question about finding the sum formula of n-th terms.
Here's the series:
$5+55+555+5555$+......
What is the general formula to find the sum of n-th terms?
My attempts:
I think I need to separate 5 from this series such…
akusaja
- 2,551
99
votes
8 answers
Intuitive meaning of Exact Sequence
I'm currently learning about exact sequences in grad sch Algebra I course, but I really can't get the intuitive picture of the concept and why it is important at all.
Can anyone explain them for me? Thanks in advance.
finnlim
- 2,733
99
votes
2 answers
Geometric way to view the truncated braid groups?
This is perhaps a vague question, but hopefully there exists literature on the subject. The question is motivated by an answer I gave to this question. I also asked a related question on MO, although hopefully this question should be easier.
There…
Dan Rust
- 30,108
99
votes
6 answers
Can the product of infinitely many elements from $\mathbb Q$ be irrational?
I know there are infinite sums of rational values, which are irrational (for example the Basel Problem). But I was wondering, whether the product of infinitely many rational numbers can be irrational.
Thank you for your answers.
Mister Set
- 1,247
98
votes
8 answers
What is $\gcd(0,0)$?
What is the greatest common divisor of $0$ and $0$?
On the one hand, Wolfram Alpha says that it is $0$;
on the other hand, it also claims that $100$ divides $0$,
so $100$ should be a greater common divisor of $0$ and $0$ than $0$.
Konstantin Weitz
- 1,265
98
votes
8 answers
Prove $\left(\frac{2}{5}\right)^{\frac{2}{5}}<\ln{2}$
Inadvertently, I find this interesting inequality. But this problem have nice solution?
prove that
$$\ln{2}>(\dfrac{2}{5})^{\frac{2}{5}}$$
This problem have nice solution? Thank you.
ago,I find…
math110
- 93,304
98
votes
6 answers
Can you make a sphere out of a plane?
I had this idea to build a model of Earth in Minecraft. In this game, everything is built on a 2D plane of infinite length and width. But, I wanted to make a world such that someone exploring it could think that they could possibly be walking on a…
986
- 1,418
98
votes
14 answers
Formal proof for $(-1) \times (-1) = 1$
Is there a formal proof for $(-1) \times (-1) = 1$? It's a fundamental formula not only in arithmetic but also in the whole of math. Is there a proof for it or is it just assumed?
tvamsisai
- 961