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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
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?
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
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
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 the result of - Mathematics Stack Exchange 3 Infinity does not lead to contradiction, but we can not conceptualize ∞ ∞ as a number The issue is similar to, what is + − × + ×, where − is the operator The answer is undefined, because + + and × × are not the kind of mathematical objects that − acts upon
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
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
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