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- One divided by Infinity? - Mathematics Stack Exchange
$\begingroup$ Arithmetic with $\infty$ is usually a convention rather than a piece of mathematics (For example, some mathematicians (in measure theory) take $\infty\cdot 0 = 0$ and reason that this should be the case since $\infty\cdot 0$ represents the "area" of an infinite line in the plane with $0$ width and hence should be $0$ since area = height$\times$ width)
- calculus - What is infinity divided by infinity? - Mathematics Stack . . .
Essentially, you gave the answer yourself: "infinity over infinity" is not defined just because it should be the result of limiting processes of different nature I e , since such a definition would be given for the sake of completeness and coherence with the fact "the limiting ratio is the ratio of the limits", your
- limits - Infinity divided by infinity - Mathematics Stack Exchange
When we use straightforward approach, we get $$ \frac{\infty+1}{\infty} = \frac{\infty}{\infty} $$ In the process of investigating a limit, we know that both the numerator and denominator are going to infinity but we dont know the behaviour of each dynamics But if we investigate further we get : $$ 1 + \frac{1}{x} $$ Some other examples :
- What exactly is infinity? - Mathematics Stack Exchange
Infinity is not a natural number, or a real number: there should be no confusion about that We can use infinity as the upper limit of an integral as shorthand to say that all the reals greater than the lower limit are included - that is a conventional use - along with others involving arbitrarily large numbers
- limits - Can I subtract infinity from infinity? - Mathematics Stack . . .
$\begingroup$ Can this interpretation ("subtract one infinity from another infinite quantity, that is twice large as the previous infinity") help us with things like $\lim_{n\to\infty}(1+x n)^n,$ or is it just a parlor trick for a much easier kind of limit? $\endgroup$ –
- Types of infinity - Mathematics Stack Exchange
$\begingroup$ "Or that the infinity of the even numbers is the same as that of the natural numbers " - not necessary This depends on your definitions I would argue the infinity of natural numbers is by 1 2 less than the infinity of even numbers (positive, negative and zero) I men, not 1 2 times, but the difference $\endgroup$ –
- Mathematical definition of infinity - Mathematics Stack Exchange
As others have noted, there are many different kinds of "infinity" used in mathematics It's sometimes easy to forget that the notion of a "number" is also somewhat ambiguous So, before you can even try to answer the question of whether infinity is a number, we need to be clear about what we mean by each term---"infinity" and also "number "
- Why is $\\infty\\times 0$ indeterminate? - Mathematics Stack Exchange
Your title says something else than "infinity times zero" It says "infinity to the zeroth power" It is also an indefinite form because $$\infty^0 = \exp(0\log \infty) $$ but $\log\infty=\infty$, so the argument of the exponential is the indeterminate form "zero times infinity" discussed at the beginning
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