# Tagged Questions

Use this tag for questions on the concept of infinity. Don't use this tag merely because $\infty$ appears somewhere in the question.

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### Refuting the Anti-Cantor Cranks

I occasionally have the opportunity to argue with anti-Cantor cranks, people who for some reason or the other attack the validity of Cantor's diagonalization proof of the uncountability of the real ...
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### First year calculus student: why isn't the derivative the slope of a secant line with an infinitesimally small distance separating the points?

I'm having trouble with the limit approach to calculus ever since I heard about the infinitesimal definition. Maybe you can help me settle what's been bothering me this year. Looking at the limit ...
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### A Puzzle on Infinity: How to guess the color of hats? [duplicate]

Infinitely many (i.e. $\omega$ - many) people each have either a white hat or black hat on their heads. Each person can see everyone's hats except their own. Each person simultaneously announces a ...
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### Compute H-infinity norm in Matlab

Please can someone write a command in Matlab for calculating $H_{\infty}$ norm for the following system: $$\frac{d}{dt}z(t)=Az(t)+Bu(t)+Fw(t)$$ $$y(t)=Cz(t)+Du(t)$$ where $A$, $B$, $C$, $D$, and $F$ ...
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### Inverse of a matrix with main diagonal elements approaching infinity

Let $A$ be a invertible, symmetric, positive definite $p \times p$ covariance matrix with main diagonal elements $a_{ii},~i = 1,~\ldots,~p$. If all main diagonal elements would approach $\infty$, ...
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### Can a curve be an asymptote?

$f(x)=x^3+\frac{3}{x-1}$ This was the question given to me. I replied that $f(x)$ will have only a single vertical asymptote of $x=1$. My teacher told that there'll be be two asymptotes. One is the ...
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### Largest infinite cardinal used in a proof

I've heard before that Knuth holds the record for the largest constant used in a mathematical proof. I was wondering what is the largest cardinal ever explicitly considered in set theory. I presume ...
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### Prove that the distance between a black and a white dot is one

I just read this article about some tough interview questions. One of the questions (allegedly given in an interview for a Technology Analyst position in Goldman Sachs) was: There are infinite ...
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### 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 ...
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### What are the limit points of $A_n=[n,\infty)$ in a metric space? Is $A_n$ closed?

$A_n=[n,\infty)$ in $\mathbb{R}$ with a Euclidean metric. A set is closed if it contains all its limit points. A limit point is a point whose neighborhood contains a point in the set. I'm not sure ...
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### Infinite differentiability with a removable discontinuity?

I'm still a beginner with calculus. But this puzzled me. Let's say you had $f(x) = \frac{x^2-1}{x+1}$. It's discontinuous at one point. If you took the derivative infinitely many times, would the ...
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### Is this sequence going to infinity, and how do we know that?

$a+\dfrac {a+\dfrac {a+\dfrac {a+\dfrac {:} {b}} {b}} {b}} {b}=?$ I've tried letting $\quad a+\dfrac {a+\dfrac {a+\dfrac {:} {b}} {b}} {b}=K$ Which makes the equation: $a+\dfrac {K} {b}=K$ $\quad$ ...
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### Why does Michio Kaku say that $\frac{1}{0} = \infty$?

Why does Michio Kaku say that $\frac{1}{0} = \infty$? http://youtu.be/AJ4zlvqOtE8?t=4m43s Instead of $\frac{1}{0}$ that's not defined, so we don't know.
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### Circle revolutions rolling around another circle

I just watched this video, and I'm a bit perplexed. Problem: ...
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In a particular problem that I am currently trying to solve, I have the following expression (this is not the entire expression, I have included only the terms involving $a_1$ and $b_1$), $\lim_{(... 1answer 32 views ### Interval notation: infinity, -infinity in closed interval I was watching a video stream a little bit ago and noticed on an equation without context that had the interval$\left[{-\infty, \infty}\right]$. This was preculiar to me as I've never seen the ... 1answer 56 views ### precise definition of a limit at infinity, application for limit at sin(x) (a) Write down the first principles definition of the statement$\lim\limits_{x→∞} f(x) = L$. For this I have that for every$ε >0$, there is a corresponding number$N$, such that if$N>0$, ... 2answers 3k views ### Must an infinite intersection of infinite sets be infinite? If$A_2$is a subset of$A_1$,$A_3$is a subset of$A_2$, and this goes on infinitely and all contain an infinite number of elements, then is the intersection from$n=1\$ to infinity, infinite as well?...
This algebra question is in Dutch and the original file van be found here: Question 19 Ill try to translate the important info needed to answer this question. $$s= \frac{(a+b)} { (ab)}$$ S= dpt ...