# Questions tagged [infinity]

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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### Is selecting a random person from an infinite population of people an invalid premise to begin with?

This was initially sparked by a hypothetical question: There are two scenarios. In the first, an infinite number of people are living in a completely blissful paradise, but every day a person is ...
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### Is a finite resource that will never run out considered infinite? [closed]

I am a regular on many SE sites, although this is my first (but hopefully not last) question on Math SE. My area of expertise is in digital technology- and although I do know more mathematical ...
1 vote
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### Brun's theorem and the twin prime conjecture

According to the following extract taken from Wikipedia, almost all prime numbers are isolated given Brun's theorem. Doesn't that mean that there is only a finite number of twin prime numbers (they ...
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### What is the meaning of "infinity" in the Continuum Hypothesis

Quoting from this article How the continuum hypothesis could have been a fundamental axiom by Joel David Hamkins: The continuum hypothesis (CH) is the assertion that the cardinality of the set of ...
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### Hyperreal valued integrals

Consider a set of real numbers $S=\{c_{\vec{x}}\}_{\vec{x}\in\mathbb{R}^3}$. That is a number for every point in 3d space. Consider the product: $$X=\prod_{\vec{x}\in\mathbb{R}^3}c_{\vec{x}}$$ In many ...
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### If I have a sequence $a_0, a_1, a_2, \cdots$ , then is expressing the limit of this sequence as $a_\omega$ sensible?

If I have a sequence created by some rule which comes to a limit , then I can express it as $a_0, a_1,a_2,\cdots$. If I said $\lim_{n \to \infty} a_n = a_{\omega}$ , is that a sensible thing to do ? ...
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1 vote
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### Is there a name for the set of lines with slopes $1$, $2$, $3$, $\ldots$?

I've recently stumbled across a pattern involving these infinite sets of lines that meet at a single point and have slopes 1, 2, 3, 4... Is there a name for these lines and have they been studied ...
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1 vote
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### A question about the number of infinities. [closed]

if there are infinite whole numbers, and there are infinite decimals between 0 and 1, and there are infinite decimals between 0.1 and 0.12, and there are infinite decimals between 0.1111111 and 0....
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### Is $\frac{1}{\sqrt{\mid x \mid}}$ integrable in interval -1 to 1?

I know that I can't integrate some unlimited functions while my interval of integration contains the singularity point. For example, $\int_{-1}^{1}\frac{1}{x}dx$ is undefined, it makes sense to me ...
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### An alternative way of looking at countable/uncountable infinities

Consider the decimal expansion of a rational number. This will either terminate, or repeat forever a finite number of its final digits. Thus, any rational number can be expressed with a finite amount ...
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1 vote
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### Ordering and dividing orders of infinity.

I read there are an infinite number of orders of infinity. Can they all be ordered, or are there different orders we can identify where we do not know which has the greater cardinality? Is the ratio ...
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### If $+\infty\leq\mu(A)$ then $\mu(A)=+\infty$

Let $(X,\mathbb{X},\mu)$ be a positive measure space. Let $A$ belong to $\mathbb{X}$. If $+\infty\leq\mu(A)$ then $\mu(A)=+\infty$. Is this statement correct? My answer is yes. I believe this is very ...
1 vote
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### why $\lim_{M\to\infty} e^{-kM}=0$

why $\lim_{M\to\infty} e^{-kM} = 0$ if $k>0$ I know that $e^{-\infty} = 0$ but why $e^{-k\infty} = 0$ I was told I could not do operations with infinity
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### Find the flaw in this mapping between the naturals and reals

I was studying Cantor's diagonal argument etc. I was testing the ideas and I thought of the following mapping between the naturals and the reals and I need some help to find the flaw in it. For ...
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### Evaluation of a limit at infinity [closed]

Evaluate $$\lim_{x \to +\infty} [\sqrt{x}-\ln(x^2+1)]$$ I tried to multiply both numerator and denominator by conjugate and tried applying L'hopital but the calculations become way too complex. Is ...
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### Does the Power of a Point Theorem apply to a point at infinity?

It is common to extend the Euclidean plane with points at infinity, one for each direction. The the theorems of Euclidean geometry generalize amazingly well to this extended plane. The Power of a ...
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### Could a sequence in the Collatz conjecture actually increase without bound?

If my understanding is correct, than the Collatz conjecture could only be false if there is at least two closed cycle in it or if there is a number which increases without bound. $3x-1$ We know that ...
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### How to interpret what a set is to see how it could be infinite?

Currently, 'infinite set' sounds oxymoronic to me, so my question is how to interpret what a set is such that it is consonant with it being infinite. I understand that we take it as axiomatic that ...
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1 vote
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### A basic question about 0 the one point compactification of $\mathbb R$

It is possible to turn the real line into a compact space by adding a single "point at infinity" which we will denote by $\infty$. The resulting compactification is homeomorphic to a circle ...
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### An apparent paradox: a different solution when transforming a linear equation

If we have $y=a(y-x)+b$, and we set $a=1$, the solution of that equation will be $x=b$. However, if we rewrite the equation as $y=\frac{a}{a-1}x-\frac{b}{a-1}$, and again we set $a=1$, we would get ...
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1 vote
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### Connecting elements in the set of Natural numbers

Lets say we "connect" two numbers in the set of Natural numbers in a way, that we draw an arrow between them. In each step we draw an arrow from a number to the number which is next to it. ...
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Suppose that we have an infinite sequence of i.i.d. binary random variables $(X_n)_n$ with $X_n\in\{0,1\}$ for all $n$ (with both options having probability 0.5). Now the outcome of all random ...