Top new questions this week:

Why do we study real numbers?

I apologize if this is a somewhat naive question, but is there any particular reason mathematicians disproportionately study the field $\mathbb{R}$ and its subsets (as opposed to any other algebraic ...

(real-analysis) (soft-question)

Are there an infinite number of prime numbers where removing any number of digits leaves a prime?

Suppose for the purpose of this question that number $1$ is a prime number. Consider the prime number $311$. If we remove one $1$ from the number we arrive at the number $31$ which is also prime. If ...

(elementary-number-theory) (prime-numbers)

I recently watched a video about different infinities. That there is $\aleph_0$, then $\omega, \omega+1, \ldots 2\omega, \ldots, \omega^2, \ldots, \omega^\omega, \varepsilon_0, \aleph_1, \omega_1, ... (cardinals) (infinity) (ordinals)  asked by KKZiomek 27 votes  answered by jaska 25 votes You have to estimate$\binom{63}{19}$in$2$minutes to save your life. This is from the lecture notes in this course of discrete mathematics I am following. The professor is writing about how fast binomial coefficients grow. "So, suppose you had 2 minutes to save your ... (combinatorics) (discrete-mathematics) (binomial-coefficients)  asked by capablanca79 27 votes  answered by Carry on Smiling 32 votes Are there theoretical applications of trigonometry? I am a high school student currently taking pre-calculus. We have just finished a unit on analytic trig. I am curious to know if there are any purely theoretical uses for trigonometry. More ... (trigonometry)  asked by Conan G. 26 votes  answered by David C. Ullrich 38 votes Can you use both sides of an equation to prove equality? For example:$\color{red}{\text{Show that}}$$\color{red}{\frac{4\cos(2x)}{1+\cos(2x)}=4-2\sec^2(x)}$$ In high school my maths teacher told me To prove equality of an equation; you start on ...

(soft-question) (proof-writing)

How do we know the ratio between circumference and diameter is the same for all circles?

The number $\pi$ is defined as the ratio between the circumeference and diameter of a circle. How do we know the value $\pi$ is correct for every circle? How do we truly know the value is the same ...

(geometry) (pi)

Greatest hits from previous weeks:

A family has three children. What is the probability that at least one of them is a boy?

According to me there are $4$ possible outcomes: $$GGG \ \ BBB \ \ BGG \ \ BBG$$ Out of these four outcomes, $3$ are favorable. So the probability should be $\frac{3}{4}$. But should you take ...

(probability)

How many squares actually ARE in this picture? Is this a trick question with no right answer?

This is one of those popular pictures on sites like Facebook. I always see a huge variation of answers such as $8, 9, 16, 17, 24, 28, 30, 40, 41, 52,$ etc., yet I've never seen a definitive answer on ...

(puzzle)

An integer sided triangle has an area $A$. Heronian triangle areas have no radical, or radical 1. Otherwise, $4 A$ will always be of the form $a\sqrt{r}$, where $r$ is the squarefree radical of the ...

(geometry) (number-theory) (recreational-mathematics) (triangle)

Measure on $\omega$ defined in the generic extension by an atomless measure algebra is atomless

Work in Cantor space with standard probability measure $m$. Suppose we are given a sequence of measurable sets $\bar{A}=\langle A_n : n\in \omega\rangle$ and a non-principal ultrafilter $U$ and the ...

(measure-theory) (set-theory)
This is a (bit funny) ultra-soft question regarded to a type of thinking that is puzzling me. Suppose $a(p_{1}, p_{2}, p_{3}, p_{4}, ... , p_{n}, Q)$ denote: from the items $p_{i}$, find a common ...