In the first limit if we plugged in x=4 we would get 0/0 and in the second limit if we “plugged” in infinity we would get ∞/−∞ (recall that as x goes to infinity a polynomial will behave in the same fashion that its largest power behaves). Infinity to the Power of Infinity. The meaning of infinity.The definition of 'becomes infinite' Let us see what happens to the values of y as x approaches 0 from the right:. This feature is not available right now. Lectures by Walter Lewin. If you raise a number of magnitude less than one to a higher power, the result is smaller. If the number is negative, when raised to the power of infinity its absolute value will approach infinity (we can't say the value is + or - b/c infinity is undefined). site design / logo © 2020 Stack Exchange Inc; user contributions licensed under cc by-sa. Also we never say what infinite to the power of zero is, we instead express such results by the use of limits: lim x→∞x1/x lim x → ∞ x 1 / x is such an expression that would be of … Viewed 2 times 0 $\begingroup$ Meant to ask thos on the other site. More specifically, "infinity" is not a member of the real number system on whicy our standard operations are defined. In calculus and other branches of mathematical analysis, limits involving an algebraic combination of functions in an independent variable may often be evaluated by replacing these functions by their limits; if the expression obtained after this substitution does not provide sufficient information to determine the original limit, then it is said to assume an indeterminate form. It's undefined. Press question mark to learn the rest of the keyboard shortcuts. One to the Power of Infinity. It's like how 0*0 is not indeterminate form. If you raise a smaller number to the same power, the result is smaller. More specifically, an indeterminate form is a mathematical expression involving $${\displaystyle 0}$$, $${\displaystyle 1}$$ and $${\displaystyle \infty }$$, 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 and thus does not yet determine the limit being sought. rev 2020.11.24.38066, MathOverflow works best with JavaScript enabled, Start here for a quick overview of the site, Detailed answers to any questions you might have, Discuss the workings and policies of this site, Learn more about Stack Overflow the company, Learn more about hiring developers or posting ads with us, removed from MathOverflow for reasons of moderation, possible explanations why a question might be removed, Homological algebra and calculus (as in Newton), Constructing a “Scattered” function over the reals, Connecting points on a variety by the image of a nonsingular curve, Conservative differential equations “in the wild”, Equation between the two branches of the lambert w function, Fundamental lemma: why is the transfer factor a power of q. It looks like from the positive data set (from the table on the right) that zero to the negative one power (0 ^ -1) approaches positive infinity. There do exist "extended" number systems in which "infinity" is defined but then the usual arithmetic operations to not apply. Ask Question Asked today. It should equal 1. New comments cannot be posted and votes cannot be cast, More posts from the NoStupidQuestions community, Press J to jump to the feed. Unfortunately, I was not able to prove what zero to the negative one power (0 ^ -1) equals. Please try again later. $\endgroup$ – Mariano Suárez-Álvarez Mar 16 '15 at 3:05 This question was removed from MathOverflow for reasons of moderation. Properties of Infinity Addition with Infinity Infinity Plus a Number Infinity Plus Infinity Infinity Minus Infinity Multiplication with Infinity Infinity by a Number Infinity by Infinity Infinity by Zero Division with Infinity and Zero Zero over a Number A Number over Zero A Number over Infinity Infinity over a Number… Why does 0.9 to the power of infinity equal 0? I thought that's impossible. Do you need to find a Maths tutor? Stack Exchange network consists of 176 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Thus you'll get a limit of zero no matter which order you take it in, and the result is completely unambiguous. If you raise a number of magnitude less than one to a higher power, the result is smaller. As the sequence of values of x become very small numbers, then the sequence of values of y, the reciprocals, become very large numbers.The values of y will become and remain greater, for example, than 10 100000000. y becomes infinite. What you want to know is «why is $\lim\limits_{x\to-\infty}e^x=0$?». Similarly, negative infinity to the negative one power (-∞ ^ -1) also approaches zero. Did you like the article? 0 raised to the power of any number always results in 0. However, they approach 1) infinity if the number is >1 and 0 if it's between 0 and 1 [0, 1) (1 to any power is 1) and 2) 0. Here are some similar questions that might be relevant: If you feel something is missing that should be here, contact us. Please refer to the help center for possible explanations why a question might be removed. Is Infinity to the power of infinity indeterminate? $\begingroup$ "Negative infinity" is not a number, so "e raised to the power of negative infinity" is nothing. Thus you'll get a limit of zero no matter which order you take it in, and the result is completely unambiguous. 1 to the power of infinity- indeterminate form evaluation. By using our site, you acknowledge that you have read and understand our Cookie Policy, Privacy Policy, and our Terms of Service. The term was originally introduced by Cauchy's student Moigno in the middle of the 19th century. It's like how 0*0 is not indeterminate form. 4.21/5 - … For the Love of Physics - Walter Lewin - May 16, 2011 - Duration: 1:01:26. Technically, both of these values are undefined. Search. If you raise a smaller number to the same power, the result is smaller. Active today. A Number to the Power of Infinity. Why does 0.9 to the power of infinity equal zero (for any number of nines)? Zero to the Power of Infinity.

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