# 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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### How can we compare a number with inifinity?

we know that $a<\infty\space\space \forall a\in\mathbb{R}$ but why? how can oder in $\mathbb{R}$ include this concept?
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### Extending our number system to include infinities [on hold]

Instead of writing infinity using the infinity symbol, could we write such numbers as: |$\mathbb Z$| (size of the set of integer numbers) |$\mathbb R$| (size of the set of real numbers) Then ...
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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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### What is meant by $\lim_{x\to \infty^+}$

I am familiar on how limits work and such. For example, look at the following limit: $$\lim_{x\to 5^+} \frac{-x^2+5x}{5-x} = 5$$ It is saying that, as $x$ approaches $5$ from the right, the equation ...
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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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### Can the extended real number $+\infty$ be compared to transfinite numbers such as $\aleph_0$?

If not, why not? If so, is ∞ greater than or less than $\aleph_0$? Edit: the discussion in comments (including comments on a deleted answer) have made me think that the best way to put the issue is ...
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### Can one non-cardinal infinity be greater than other non-cardinal infinity?

As far as I know, there are two different notions to the word "infinity" in Mathematics. First notion of infinity has to do with the cardinality of a set: if a set contains infinite number of ...
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### Set theory with multiple countable infinities [closed]

In set theory, all sets that are countably infinite are generally considered to have the same size since there is a bijection between them. Has anyone tried formalising set theory in a way which ...
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### If $\dfrac{1}{\infty}=0$ then I can prove that $0 = 1$ [closed]

Given, $\dfrac{1}{\infty}=0$, then $1=0 \cdot \infty = 0$ (because $0$ times any number or values is $0$ and here that number is infinity). Which gives us $1=0$ i.e, $0=1$. Hence proved....
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### Voronoi edges example

I have 4 line segments: 0 0 2 0 // 1st line segment 2 0 2 1 // 2nd line segment 2 1 0 1 0 1 0 0 and I wrote some CGAL code to print the Voronoi edges. However, <...
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### How many points in a line segment?

My teacher said that in the circumference of circle there are infinite points. When I was learning more about circle, I came to this picture: My question is: When we unroll the circle, then the ...
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### Is there an infinity smaller than countable? [duplicate]

In other words: is $\aleph_0$ the smallest infinity? Is it easy to prove?
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### Random Room changing in the Hilbert hotel. [closed]

Let's say you have a Hilbert's grand hotel full occupancy. Assign each occupant a new room select randomly without regard to whether the room is assigned to someone. i.e. empty rooms, multiple ...
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### Flea on the coordinate system

We drop a flea on a point of the coordinate system(with integer coordinates). Due to the dimensions of the flea we can not see it. The flea jumps away every second by one unit (always in the same ...
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### Complex variable limit at infinity

Is $\lim\limits_{z\to\infty} \frac{4z^2}{(z-1)^2}$, $z\in\mathbb{C}$, evaluated the same way as a real variable function limit? Or does one need to show separate cases for $x\to\infty$ and $y\to\infty$...
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### Will a decreasing probability ever resolve favorably? [duplicate]

Let's say I start off with a 50/50 chance at winning the lottery. But I lose. Now my chance is only half as good, or 25%. I lose again. Now the chance is 12.5%. Same result. If this continues all ...
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### Find a **bijection** between two intervals

I am struggling with this question and was hoping somebody could help me, Thanks Find a bijection between the intervals $(-1,1)$ and $(0,4)$ where $X \in R$
I was watching Ramanujan: Making sense of 1+2+3+... = -1/12, where the presenter writes: (I tried to write this out in $\LaTeX$ but couldn't figure out how to do multi-column alignment without ...