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What is infinity divided by infinity? - Mathematics Stack Exchange I know that $\infty \infty$ is not generally defined However, if we have 2 equal infinities divided by each other, would it be 1? if we have an infinity divided by another half-as-big infinity, for
What exactly is infinity? - Mathematics Stack Exchange Definition: Infinity refers to something without any limit, and is a concept relevant in a number of fields, predominantly mathematics and physics The English word infinity derives from Latin infinitas, which can be translated as " unboundedness ", itself derived from the Greek word apeiros, meaning " endless "
Can I subtract infinity from infinity? - Mathematics Stack Exchange 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?
Why is $\infty\times 0$ indeterminate? - Mathematics Stack Exchange In particular, infinity is the same thing as "1 over 0", so "zero times infinity" is the same thing as "zero over zero", which is an indeterminate form Your title says something else than "infinity times zero" It says "infinity to the zeroth power"
One divided by Infinity? - Mathematics Stack Exchange Similarly, the reals and the complex numbers each exclude infinity, so arithmetic isn't defined for it You can extend those sets to include infinity - but then you have to extend the definition of the arithmetic operators, to cope with that extended set And then, you need to start thinking about arithmetic differently
What is imaginary infinity, $i\lim\limits_ {x \to \infty} x = i\infty$? The infinity can somehow branch in a peculiar way, but I will not go any deeper here This is just to show that you can consider far more exotic infinities if you want to Let us then turn to the complex plane The most common compactification is the one-point one (known as the Riemann sphere), where a single infinity $\tilde\infty$ is added
What is the square root of infinity and what is infinity^2? Thus both the "square root of infinity" and "square of infinity" make sense when infinity is interpreted as a hyperreal number An example of an infinite number in $ {}^\ast \mathbb R$ is represented by the sequence $1,2,3,\ldots$
Why is $1^ {\infty}$ considered to be an indeterminate form 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 Hence, indeterminate form