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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 "
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
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
soft question - Why is $\infty \cdot 0$ not clearly equal to $0 . . . (i e add 0 0 to 0 0 as many times as you like, result is 0 0) So I thought an infinite number of 0 0 's cannot be anything but 0 0? But someone claims different but couldn't offer a reasonable explanation why Google results seemed a bit iffy on the subject - hopefully this question will change that
What is imaginary infinity, - Mathematics Stack Exchange 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 ∞~ ∞ is added
Types of infinity - Mathematics Stack Exchange I understand that there are different types of infinity: one can (even intuitively) understand that the infinity of the reals is different from the infinity of the natural numbers Or that the infi
definition - Is infinity a number? - Mathematics Stack Exchange For infinity, that doesn't work; under any reasonable interpretation, $1+\infty=2+\infty$, but $1\ne2$ So while for some purposes it is useful to treat infinity as if it were a number, it is important to remember that it won't always act the way you've become accustomed to expect a number to act
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 does e raised to the power of negative infinity equal 0? Why is it that e raised to the power of negative infinity would equal 0 instead of negative infinity? I am working on problems with regards to limits of integration, specifically improper integrals
infinity - Are all infinities equal? - Mathematics Stack Exchange A friend of mine was trying to explain to me how all infinities are equal For example, they were saying that there are the same amount of numbers between $0$–$1$ as there are between $0$–$2$ The