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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
Why is $\\infty\\times 0$ indeterminate? - Mathematics Stack Exchange "Infinity times zero" or "zero times infinity" is a "battle of two giants" Zero is so small that it makes everyone vanish, but infinite is so huge that it makes everyone infinite after multiplication 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
What is the meaning of infinity in the Continuum Hypothesis The continuum hypothesis (CH) is the assertion that the cardinality of the set of real numbers is the first uncountable infinity, or in other words, that $2^ {\aleph_0} = \aleph_1$
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
infinity - Is $\infty$ undefined? - Mathematics Stack Exchange Infinity does not exist in the typical real number line: it is a construct that is contained in the extended real number line, which is used in certain fields of mathematics, especially limit calculus
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
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 limn→∞(1+x n)n, lim n → ∞ (1 + x n) n, or is it just a parlor trick for a much easier kind of limit?
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