In that case infinity to the power of zero is 1 because any Real NUMBER to the power zero is 1. If you extend the Real numbers set, you may say that infinity is defined as the NUMBER, which is bigger than any of the numbers in the non-extended Real numbers set. In general, infinity just means continues forever. But when you calculate limits, infinity to the power zero is indeterminate. In these cases, a particular operation can be performed to solve each of the indeterminate forms . Sign up for an online college math course at http://www.straighterline.com/online-college-courses/mathematics/ Indeterminate Form Infinity to 0 More specifically, an indeterminate form is a mathematical expression involving , and ∞, obtained by applying the algebraic limit theorem in the process of attempting to determine a limit, which fails to restrict that limit to one specific value or infinity (if a limit is confirmed as infinity, then it is not interminate since the limit is determined as infinity) and thus does not yet determine the limit being sought. Why … Infinity is not a number, but zero is at the center of all numbers. One to the Power of Infinity An indeterminate form does not mean that the limit is non-existent or cannot be determined, but rather that the properties of its limits are not valid. When dealing with ratios such as 1/0, 0/0, or infinity in any form, you will most likely need to use a further theorem, such as L’Hopital’s, to solve for a limit. Indeterminate forms hover over the calculus no matter where you turn. Numbers spread to infinity in all directions from zero.
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