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.

A lay person might think they know what infinity is, but a mathematician will ask you "what kind of infinity are you talking about, and in what context?"

See the question Is Infinity a number and in particular this answer for a good discussion on a number of things that people sometimes mean when they talk about "infinity" in mathematical terms.

Good questions about infinity will need to be explicit about the context in which the question is being asked; many of the questions already tagged essentially have the answer "The answer is undefined, because infinity isn't an ordinary number" or "Your question can't be answered without giving more information." And there is probably already a different tag covering whatever field of mathematics the question is about.

Please check the questions What is the result of $\infty-1$? and What is the result of infinity minus infinity? before asking questions about doing arithmetic on infinity.

Questions about fallacies involving infinity are on-topic for this tag.

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Is [0.1, 1[ countable? (Or, why can a decimal number have an infinite of digits, but a whole number cannot?)

Note: I'm not asking about [0,1], I'm explicitly asking about [0.1, 1]. I'm being told [0.1, 1] is not countable. It's clear for me that [0,1] isn't, but it feels less clear for [0.1, 1], and I'll try to explain my understanding: Essentially the…
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Do mathematicians really use infinity in their computations?

I say that mathematicians use the words infinity and infinite, but in their computations they change the meanings of infinity and infinite, so that they are no longer with the meanings of without end, but with end, and it is because they cannot…
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Does the use of infinity imply or is shorthand for a limit to infinity

So, is $\frac{1}{\infty}$ shorthand for $\lim_{x\to\infty} \frac{1}{x}$ like an improper integral implies a limit being infront of it?
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A Question about Infinity Values

I have a question that has been bugging me since last night. Let's say we have a car travelling at $5$ms$^{-1}$ at one instant. From $5$ms$^{-1}$ it accelerates uniformly to $6$ms$^{-1}$ in $2$ seconds. How do I wrap my head around the fact that…
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What is the highest order of infinity?

I know there are countably infinite sets and uncountably infinity sets. I would like to know, what is the highest order of infinity?
ktm5124
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$\lim_{n\to 1}(\frac{1}{1-n})=\infty$

$\lim_{n\to 1}(\frac{1}{1-n})=\infty$ When $n=1$, the equation, of course, becomes undefined, as it becomes $\frac10$ I know this can be proven since $\frac{1}{1-n}=\sum_{k=0}^{\infty}n^k$, which would make…
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What is the definition of $\bigcup_{i}^{\infty}A_i$ and $\sum_{i}^{\infty}a_i$?

What is the definition of $\bigcup_{i}^{\infty}A_i$ and $\sum_{i}^{\infty}a_i$? My assumption until now was $$\bigcup_{i}^{\infty}A_i=\lim_{n\rightarrow\infty}\bigcup_{i}^{n}A_i$$ and…
user675768
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The difference between "goes to infinity" and "goes off to infinity"?

I am currently reading the book ''The Outer Limits of Reason'' and encountered a description about which I am very confused. I am afraid to say, this may be due to the fact that I am not a native English speaker. on pp.61, it says: Again there is a…
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Does the set ω + 1 represent a higher infinity that ω? In other words, is ω + 1 countable? What about ω +ω?

I answered the first part as follows: $\omega + 1 = \{0, 1, 2, 3, 4, 5, ..., \omega\} = \aleph_0 $ Since every element of ω is finite and one element in $\omega + 1$ is infinite, they are clearly different infinite numbers. This is also known…
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Why is counting with infinity not indeterminable?

I was trying to find a function that looks like square root of x but I wanted to limit that function from above to 1. Finding solution was not as hard as I thought, but... When I was thinking about solution I was thinking about infinity, because…
vbargl
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What is $(1/0)^{-1}$?

What is $(\frac{1}{0})^{-1}$? Would the fraction be reciprocated first to give you $\frac{0}{1}=0$. Or would you not be able to evaluate this as $\frac{1}{0}$ is undefined?
Jamminermit
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The linear slope of a parabola function over one to infinity

I have come across something which is most likely wrong. If there is a better place to put this, please tell me. Also, please let me know why it is wrong. Taking the linear slope of the parabola function $f(x) = x^2$ with…
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How to show those sets being countable or uncountable?

Consider the following questions, how do I show countability of set $A$ and $B$? (a) A subset $A$ of $\mathbb{R}$ has the property that, given $\varepsilon > 0$ and $x \in \mathbb{R}$, there exist $a,b \in \mathbb{R}$ with $a \in A$ and $b \not \in…
TYjhcvb
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Prove equivalence of the following definitions of Dedekind-finiteness

I'm trying to prove the equivalence of the following two (weaker) definitions of finiteness. I know that these definitions are equivalent to the standard definition of finiteness if the axiom of choice holds, but I'm trying to prove they are…
user308485
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What is the solution to the random version of the "Farmers and Pesky Birds" problem from "Math Fun Facts"?

Here's the text of the problem: Alice and Bob are two farmers each wanting to plant a (countably infinite) row of seeds, side by side in a field. Both of them have pesky birds that hinder their efforts in funny ways. As Alice walks along the row,…