Top new questions this week:
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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:
$$\frac{a+b}{b} ...
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To reiterate the question, basically there is some number, $n$ that exists that is divisible all the integers $1, \dots, 200$, except for two consecutive numbers in that range. The goal is to find ...
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I am beginning real analysis and got stuck on the first page (Peano Postulates). It reads as follows, at least in my textbook.
Axiom 1.2.1 (Peano Postulates). There exists a set $\Bbb N$ with an ...
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Removing finitely many point from an open set in $\mathbb{R}^n$ gives an open set. Is this true in general for any space?
My intuition is that this is the case, however, how does one (dis)prove ...
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Suppose we have defined the "cochord" of an angle $\theta \in (-\pi,\pi)$ as
$$\operatorname{coc}(\theta) := 2\cos\left(\frac \theta 2\right),$$
and set
$$c_n := \frac 1 \pi \int_{-\pi}^{\pi} \ln^n ...
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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&
\\ ...
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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 ...
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Greatest hits from previous weeks:
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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 $1000$ ...
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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 ...
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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.
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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.
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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 ...
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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 ...
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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 $9$ ...
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Can you answer these questions?
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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 ...
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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 ...
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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 ...
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