# Most Popular

1500 questions

**329**

votes

**0**answers

### Limit of sequence of growing matrices

Let
$$
H=\left(\begin{array}{cccc}
0 & 1/2 & 0 & 1/2 \\
1/2 & 0 & 1/2 & 0 \\
1/2 & 0 & 0 & 1/2\\
0 & 1/2 & 1/2 & 0
\end{array}\right),
$$
$K_1=\left(\begin{array}{c}1 \\ 0\end{array}\right)$ and consider the sequence of matrices defined by
$$
K_L =…

Eckhard

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**319**

votes

**31**answers

### Nice examples of groups which are not obviously groups

I am searching for some groups, where it is not so obvious that they are groups.
In the lecture's script there are only examples like $\mathbb{Z}$ under addition and other things like that. I don't think that these examples are helpful to…

Dominic Michaelis

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**308**

votes

**6**answers

### Multiple-choice question about the probability of a random answer to itself being correct

I found this math "problem" on the internet, and I'm wondering if it has an answer:
Question: If you choose an answer to this question at random, what is the probability that you will be correct?
a. $25\%$
b. $50\%$
c. $0\%$
d. $25\%$
Does this…

user11088

**304**

votes

**8**answers

### Intuition for the definition of the Gamma function?

In these notes by Terence Tao is a proof of Stirling's formula. I really like most of it, but at a crucial step he uses the integral identity
$$n! = \int_{0}^{\infty} t^n e^{-t} dt$$
, coming from the Gamma function. I have a mathematical…

Qiaochu Yuan

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- 42
- 777
- 1,145

**302**

votes

**5**answers

### In Russian roulette, is it best to go first?

Assume that we are playing a game of Russian roulette (6 chambers) and that there is no shuffling after the shot is fired.
I was wondering if you have an advantage in going first?
If so, how big of an advantage?
I was just debating this with…

nikkita

- 2,669
- 2
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- 5

**297**

votes

**39**answers

### One question to know if the number is 1, 2 or 3

I've recently heard a riddle, which looks quite simple, but I can't solve it.
A girl thinks of a number which is 1, 2, or 3, and a boy then gets to ask just one question about the number. The girl can only answer "Yes", "No", or "I don't know," and…

Gintas K

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**297**

votes

**18**answers

### Why does this innovative method of subtraction from a third grader always work?

My daughter is in year $3$ and she is now working on subtraction up to $1000.$ She came up with a way of solving her simple sums that we (her parents) and her teachers can't understand.
Here is an example: $61-17$
Instead of borrowing, making it…

Alice

- 2,117
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**294**

votes

**16**answers

### Math without pencil and paper

For someone who is physically unable to use a pencil and paper, what would be the best way to do math?
In my case, I have only a little movement im my fingers. I can move a computer mouse and press the left button. Currently I do very little math…

Jeroen

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**294**

votes

**9**answers

### V.I. Arnold says Russian students can't solve this problem, but American students can -- why?

In a book of word problems by V.I Arnold, the following appears:
The hypotenuse of a right-angled triangle (in a standard American examination) is 10 inches, the altitude dropped onto it is 6 inches. Find the area of the triangle.
American…

Eli Rose

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**293**

votes

**28**answers

### In the history of mathematics, has there ever been a mistake?

I was just wondering whether or not there have been mistakes in mathematics. Not a conjecture that ended up being false, but a theorem which had a proof that was accepted for a nontrivial amount of time before someone found a hole in the argument.…

Steven-Owen

- 5,296
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**291**

votes

**21**answers

### Really advanced techniques of integration (definite or indefinite)

Okay, so everyone knows the usual methods of solving integrals, namely u-substitution, integration by parts, partial fractions, trig substitutions, and reduction formulas. But what else is there? Every time I search for "Advanced Techniques of…

user3002473

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**291**

votes

**22**answers

### Why can ALL quadratic equations be solved by the quadratic formula?

In algebra, all quadratic problems can be solved by using the quadratic formula. I read a couple of books, and they told me only HOW and WHEN to use this formula, but they don't tell me WHY I can use it. I have tried to figure it out by proving…

idonno

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**286**

votes

**42**answers

### Can't argue with success? Looking for "bad math" that "gets away with it"

I'm looking for cases of invalid math operations producing (in spite of it all) correct results (aka "every math teacher's nightmare").
One example would be "cancelling" the 6's in
$$\frac{64}{16}.$$
Another one would be something like
$$\frac{9}{2}…

kjo

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**285**

votes

**24**answers

### Is mathematics one big tautology?

Is mathematics one big tautology? Let me put the question in clearer terms:
Mathematics is a deductive system; it works by starting with arbitrary axioms, and deriving therefrom "new" properties through the process of deduction. As such, it would…

Coffee_Table

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**285**

votes

**9**answers

### Is a matrix multiplied with its transpose something special?

In my math lectures, we talked about the Gram-Determinant where a matrix times its transpose are multiplied together.
Is $A A^\mathrm T$ something special for any matrix $A$?

Martin Ueding

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