# 0 to the power of infinity

A Number to the Power of Infinity. Ask Question Asked today. It's like how 0*0 is not indeterminate form. The term was originally introduced by Cauchy's student Moigno in the middle of the 19th century. What you want to know is «why is $\lim\limits_{x\to-\infty}e^x=0$?». $\endgroup$ – Mariano Suárez-Álvarez Mar 16 '15 at 3:05 Do you need to find a Maths tutor? This feature is not available right now. Viewed 2 times 0 $\begingroup$ Meant to ask thos on the other site. Press question mark to learn the rest of the keyboard shortcuts. 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. 4.21/5 - … Please try again later. Lectures by Walter Lewin. This question was removed from MathOverflow for reasons of moderation. Similarly, negative infinity to the negative one power (-∞ ^ -1) also approaches zero. New comments cannot be posted and votes cannot be cast, More posts from the NoStupidQuestions community, Press J to jump to the feed. It should equal 1. 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:. $\begingroup$ "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. Zero to the Power of Infinity. If you raise a number of magnitude less than one to a higher power, the result is smaller. Thus you'll get a limit of zero no matter which order you take it in, and the result is completely unambiguous. I thought that's impossible. If you raise a smaller number to the same power, the result is smaller. 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. Technically, both of these values are undefined. 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). 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 … Active today. If you raise a number of magnitude less than one to a higher power, the result is smaller. 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… More specifically, "infinity" is not a member of the real number system on whicy our standard operations are defined. Search. 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). Did you like the article? For the Love of Physics - Walter Lewin - May 16, 2011 - Duration: 1:01:26. 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. There do exist "extended" number systems in which "infinity" is defined but then the usual arithmetic operations to not apply. 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. Why does 0.9 to the power of infinity equal 0? If you raise a smaller number to the same power, the result is smaller. It's undefined. Please refer to the help center for possible explanations why a question might be removed. Is Infinity to the power of infinity indeterminate? 1 to the power of infinity- indeterminate form evaluation. site design / logo © 2020 Stack Exchange Inc; user contributions licensed under cc by-sa. 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. 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's like how 0*0 is not indeterminate form. 0 raised to the power of any number always results in 0. One to the Power of Infinity. Here are some similar questions that might be relevant: If you feel something is missing that should be here, contact us. Why does 0.9 to the power of infinity equal zero (for any number of nines)? Unfortunately, I was not able to prove what zero to the negative one power (0 ^ -1) equals. Thus you 'll get a limit of zero no matter which order you take it in and. Similar questions that might be relevant: if you raise a smaller number to the one... 0.9 to the power of any number of nines ) number to the power of infinity equal 0 want... This question was removed from MathOverflow for reasons of moderation matter which order take... Question was removed from MathOverflow for reasons of moderation smaller number to the power of any number results... 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