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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
Can I subtract infinity from infinity? - Mathematics Stack Exchange $\begingroup$ 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? $\endgroup$ –
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)
Why is $1^{\\infty}$ considered to be an indeterminate form The indeterminate forms are often abbreviated with stuff like "$1^\infty$" but that's not what they mean This "$1^\infty$" (in regards to indeterminate forms) actually means: when there is an expression that approaches 1 and then it is raised to the power of an expression that approaches infinity we can't determine what happens in that form
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
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 $\endgroup$ –
Is $0^\infty$ indeterminate? - Mathematics Stack Exchange (In the framework of the projectively extended real line, the limit is the unsigned infinity $\infty$ in all three cases )" $\endgroup$ – user236182 Commented Sep 16, 2017 at 23:50