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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
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 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 "
limits - Infinity divided by infinity - Mathematics Stack Exchange 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 But if we investigate further we get : 1 + 1 x Some other examples : Numerator might get larger than denomenator exactly m times The limit will be m : for example lim mx x
Mathematical definition of infinity - Mathematics Stack Exchange Another way "infinity" is used is to describe the size of sets There are an infinite number of integers, and also an infinite number of even integers, and also an infinite number of prime integers, not to mention rational numbers (fractions), or even the set of all polynomials
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
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?
What is the result of - Mathematics Stack Exchange In "the end," infinity does not have an end" you have given all coins away and so the balance is 0 0 The difference between the two scenarios is, in the second the order of the coins is preserved, in the first the coins are piled and one only looks at the total value of the coins
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 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