Mathematics Stack Exchange Community Digest

Top new questions this week:

Why does this process map every fraction to the golden ratio?

Start with any positive fraction $\frac{a}{b}$. First add the denominator to the numerator: $$\frac{a}{b} \rightarrow \frac{a+b}{b}$$ Then add the (new) numerator to the denominator: $$\frac{a+b}{b} ...

sequences-and-series golden-ratio  
asked by Joseph O'Rourke 32 votes
answered by Brady Gilg 73 votes

There is a number divisible by all integers from 1 to 200, except for two consecutive numbers. What are the two?

To reiterate the question, basically there is some number, $n$ that exists that is divisible all the integers $1, \dots, 200$, except for two consecutive numbers in that range. The goal is to find ...

elementary-number-theory prime-numbers divisibility gcd-and-lcm  
asked by Slade 20 votes
answered by slbtab 40 votes

How does Peano Postulates construct Natural numbers only?

I am beginning real analysis and got stuck on the first page (Peano Postulates). It reads as follows, at least in my textbook. Axiom 1.2.1 (Peano Postulates). There exists a set $\Bbb N$ with an ...

natural-numbers peano-axioms  
asked by Solomon Tessema 14 votes
answered by Ethan Bolker 30 votes

Does removing finitely many points from an open set yield an open set?

Removing finitely many point from an open set in $\mathbb{R}^n$ gives an open set. Is this true in general for any space? My intuition is that this is the case, however, how does one (dis)prove ...

general-topology separation-axioms  
asked by Stephen 14 votes
answered by Maximilian Janisch 19 votes

How are the logarithmic integrals $\int_{-\pi}^{\pi} \ln^n(2\operatorname{cos}(x/2))dx$ related to $\zeta(n)$?

Suppose we have defined the "cochord" of an angle $\theta \in (-\pi,\pi)$ as $$\operatorname{coc}(\theta) := 2\cos\left(\frac \theta 2\right),$$ and set $$c_n := \frac 1 \pi \int_{-\pi}^{\pi} \ln^n ...

integration fourier-series riemann-zeta  
asked by giobrach 12 votes
answered by Szeto 10 votes

Is there any intuition why the following matrix is positive semidefinite?

I have the following 8 by 8 square matrix, which is positive semidefinite: \begin{bmatrix}3&1&1&-1&1&-1&-1&-3\\1&3&-1&1&-1&1&-3&-1& \\ ...

linear-algebra matrices symmetric-matrices positive-semidefinite  
asked by Jiguang Li 12 votes
answered by A.Γ. 15 votes

Suppose that $x^5$ and $20x+\frac {19}x$ are rational numbers. Then $x$ is also rational

Let $x\neq0$ be a real number such that $x^5$ and $20x+\frac {19}x$ are rational. How can we prove that $x$ is also rational? (This was a question from the RMO 2019 in India.) My attempt: Let ...

contest-math roots rational-numbers  
asked by StackUnderflow 11 votes
answered by Krishnarjun 11 votes

Greatest hits from previous weeks:

A loss and gain problem

This is a very simple but confusing puzzle. A customer buys goods worth $200$ rupees from a shop. The shopkeeper selling these goods makes zero profit from this purchase. The lady gives him a $1000$ ...

asked by constantlearner 8 votes
answered by fgp 8 votes

why does e raised to the power of negative infinity equal 0?

Why is it that e raised to the power of negative infinity would equal 0 instead of negative infinity? I am working on problems with regards to limits of integration, specifically improper integrals ...

calculus limits exponentiation infinity  
asked by apple.pi 8 votes
answered by DeepSea 14 votes

What does "∈" mean?

I have started seeing the "∈" symbol in math. What exactly does it mean? I have tried googling it but google takes the symbol out of the search.

asked by Locke 40 votes
answered by Hippalectryon 43 votes

Derivative of square root

What would be the derivative of square roots? For example if I have $2 \sqrt{x}$ or $\sqrt{x}$. I'm unsure how to find the derivative of these and include them especially in something like implicit.

calculus derivatives  
asked by soniccool 20 votes
answered by Brian M. Scott 24 votes

Finding two numbers given their sum and their product

Which two numbers when added together yield $16$, and when multiplied together yield $55$. I know the $x$ and $y$ are $5$ and $11$ but I wanted to see if I could algebraically solve it, and found ...

algebra-precalculus systems-of-equations  
asked by Kyle H 10 votes
answered by Joe 12 votes

How to find perpendicular vector to another vector?

How do I find a vector perpendicular to a vector like this: $$3\mathbf{i}+4\mathbf{j}-2\mathbf{k}?$$ Could anyone explain this to me, please? I have a solution to this when I have ...

linear-algebra geometry vector-spaces vectors  
asked by niko 55 votes
answered by carlop 47 votes

How many times are the hands of a clock at $90$ degrees.

How many times are the hands of a clock at right angle in a day? Initially, I worked this out to be $2$ times every hour. The answer came to $48$. However, in the cases of $3$ o'clock and $9$ ...

geometry puzzle  
asked by iajnr 9 votes
answered by Harald Hanche-Olsen 14 votes

Can you answer these questions?

Equation-to-Text Converter

I was just thinking today... I was reading a book called "Forecasting: Principles and Practice", and found myself reading mostly the theoretical paragraphs, and skipping most of the mathematical ...

asked by Hassaan 1 vote

Collatz Conjecture Numbers up to n

I was playing around with the Collatz sequences of numbers up to a number. My question was, for which numbers $n$ does no integer below $n$ reach $n$ in its iteration? So I wrote a program to find ...

number-theory collatz  
asked by TigerGold 1 vote

Functional Analysis study reference requests.

I’m currently studying for an exam in Functional analysis. I have already gone through my homework assignments and lecture notes and would like to practice some more problems. My professor isn’t ...

functional-analysis reference-request self-learning  
asked by Zed1 1 vote
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