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.

2415 questions
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Is the number of points on a plane larger than the number of points on a line?

The number of points on a line is uncountably infinite. The number of lines on a plane is uncountably infinite. It seems like it follows that there would be an uncountably infinite number of points on a plane, too. But it seems unsatisfying to…
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Is the spacing between the set of all natural number powers bounded?

I was wondering whether the set of all numbers that can be expressed as a natural number to the power of another natural number has "infinitely wide" gaps or if there is some upper bound between the distance between two neighboring elements. Or, put…
user90667
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Is this set countably infinite or not?

"Far away, in the heavenly abode of the great god Indra, there is a wonderful net that has been hung by some artificer in such a manner that it stretches out infinitely in all directions. In accordance with the extravagant tastes of deities, the…
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What is infinity times the reciprocal of infinity?

I was talking with a friend about interesting properties of numbers and their theoretical contradictions and solutions when we came up with this. What is the answer? So... $x * ∞ = ∞$ and... $\frac{1}{x}*x=1$ So what do you get when you…
JShoe
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Why are these expressions indeterminate expressions?

Why are these $1^\infty,$ $0\cdot\infty$ and $\infty^0$ indeterminate forms. Why we can't solve these expressions?
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cantor's diagonalization argument (multiple sizes of infinities)

Yes, many people have asked the same question, and I have tried by best to get my head around it, but I still can't understand. Every time I look at the proofs, they seem like a sleight of hand to me.. Kindly point out the faults in my…
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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.
user8005
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Multiples of numbers up to infinity

A question my wife and I were chatting about last night. Are there more multiples of 3 than there are of 17, if we count from 0 to infinity One point of view was since there are infinite multiples of 3 and infinite multiples of 17, the number of…
bobby
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Can I have visited all rooms of Hilbert's infinite hotel?

Thanks in advance for any helpful comments! As this is all theory and abstract, please don't leave comments about the practicality of this (unless you feel that it is really relevant). Comments like "infinity is an impossibility anyway" don't really…
Kaktus
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Is infinite a infinite or finite

Long back I have watched a documentary based on a mathematician named Cantor. According to that documentary, Cantor claimed that infinite does not exists, it is only finite. Is that True?
VAR121
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Theory about infinity

Is there any theory that takes account of the difference in, for example, $1 \over 0$ and $-\ln 0$ and treat them as different infinities with different notations (and maybe useful theorems)? Cantor's theory only specializes in set cardinality but…
cr001
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How does it equal -1/12?

So all my friends keep telling me that if you add up all the numbers from 1 to infinity, (1+2+3+4...) then the answer is -1/12. They showed me this proof with infinite sums, but I didn't understand it, so all I'm asking is does it really equal…
Parzival
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Less than infinity or Less or Equal to infinity

What is the difference between Less than infinity or Less or Equal to infinity? We cannot substitute infinity anyway, and have to use limits. So does it make sense to write less and equal to infinity?
superM
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Does negative infinity squared = positive infinity?

I googled this question and saw this answer but I wasn't satisfied.
Squirrl
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What is infinity in complex plane and what are operation with infinity extended to complex numbers?

For a real number $a$, $$\infty + a = \infty,$$ and if $a$ is positive, $$\infty \cdot a = \infty$$ What is $\infty + a$ and $\infty*a$ if $a$ is non-zero complex number, where $\infty$ is real positive infinity?
Harsh
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