My answer is not scientific or mathematic but I think of it this way: Imagine if I asked you to write it out for me...... you would write 1x1x1x1x1x1x1x1........for ever and never reach the equal sign. That series diverges, so the limit doesn't exist. Looks like you're using new Reddit on an old browser. I can see the logic of the first answer and it makes sense, but real answer can never be determined because infinity does not stop. Because it is 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 .... x 1. Depending on the rate and direction at which we try to approach 1∞, we get wildly different results. 2. why 1/ infinity isn't indeterminate like other indeterminate? It is the opposite of finite. Get your answers by asking now. By signing up, you'll get thousands of step-by-step solutions to your homework questions. 12 hours ago. Formally: A sequence (a_n) converges to infinity (or diverges) if for all natural numbers M there exists an natural number N such that n>N implies that a_n>M. One positive integer is 7 less than twice another. In other words our mathematical division has failed. Q.E.D. Seeing how 1 x 1 x 1 x 1....... = 1, why is 1∞ indeterminate? For example let try to divide say 4 by zero.IE dividend=4,divisor=zero, what would be the quotient? For example 1*∞ is determinate; 1*∞ = ∞ in all cases. Ask Question Asked 1 year, 1 month ago. When we search for the limit of a function, we can sometimes determine surely how it will act towards infinity. 1 to the power of anything still equals to 1. saying that 0 • ∞ is indeterminate means that one cannot adjoin ∞ to the real numbers and get a system with well-defined notions of addition and multiplication. Viewed 91 times 1 $\begingroup$ $1/\infty$ tends to 0. What is infinity? Infinity is a concept introduced to take care of events during which normal rules of mathematics breakdown. 1 x 1 x 1 ... is 1. save hide report. So we say the quotient is infinity. Perhaps you meant the indeterminate form ##[1^\infty]## (written in brackets to emphasize that this is an indeterminate form). Indeed this can be grossly wrong as the fundamental example If the area of a rectangular yard is 140 square feet and its length is 20 feet. So logically you can never arrive at the result because ∞ never ends. 1 to the power of "everything or anything" is still 1. Infinity is a concept not a number. A limit of the form 1∞ can be 1, ∞ or some value in-between which makes 1∞ indeterminate. These aren't "maths tricks" or approximations, I'd recommend at least looking at the Wikipedia page to get a basic understanding of what indeterminism is. So why is indertiminate? There is a Numerical Method and general proof to see why it is an indeterminate, but the math is a bit complicated. 1^1=1,1^2=1,1^3=1................upto 1^infinity. How do you think about the answers? one way to look at this is to write 1 = exp{0}. Pelosi on virus deaths: 'This was preventable' 'Curviest model ever' in bid to change fashion industry Tony Hsieh, iconic Las Vegas entrepreneur, dies at 46, A boxing farce: Ex-NBA dunk champ quickly KO'd, Jolie becomes trending topic after dad's pro-Trump rant, 2 shot, killed at Northern Calif. mall on Black Friday, Harmless symptom was actually lung cancer, Eric Clapton sparks backlash over new anti-lockdown song, Highly conservative state becomes hot weed market, Black Friday starts off with whimper despite record day, No thanks: Lions fire Matt Patricia, GM Bob Quinn, How the post-election stocks rally stacks up against history, Reynolds, Lively donate $500K to charity supporting homeless. or an INDETERMINATE that which cannot be determined. So logically you can never arrive at the result because ∞ never end. But that value is not the limit. " indeterminate" means that from the behavior of the functions involved you can't say,without further calculation the existence or value of the limit. Firstly, I should point out that ∞ and determinism aren't mutually exclusive. Cause infinity is a concept not a number. The simplest answer is that many limits are of the form 1∞ but tend to different values. By signing up, you'll get thousands of step-by-step solutions to your homework questions. 1^2, you stop at the second multiple. This is why mathematics is beautyful and so related to phylosophical issues... 1^infty is indeterminate but it aproaches 1 in the limit (how does that sound?). There is no way to exponentiate 1 which returns a non-1 result, since 1*anything = anything. Still have questions? 1. Obviously an expression involving an indeterminate will again result (in this case) to be an indeterminate. Therefore this limit is equal to 1. Real analysis handles infinities with quantities getting increasingly large. Join Yahoo Answers and get 100 points today. The sum of their squares is 145? Is this right or should I change the exponents? The answer will always remain 1 no matter how many times you multiply. 1 times "anything and everything" is still "anything and everything". $\mathbf {It\ doesn't \ satisfy\ the\ inverse \ process\ of\ multiplication \ and \\division\ i.e} $ $\infty * 0$ is undefined or indeterminate. 4 years ago. the answers that say 1^∞ = 1 also have a point, since, 1^∞ = (limit as n → ∞ of 1^n) = 1. in the same way, one. Close. Sharon Stone reveals co-star who was the best kisser. In both cases the fraction involving n becomes infinitely small and the power becomes infinitely big, which means they are both of the form 1∞. Why is infinity^0 indeterminate, but 0^infinity not. In limits what you see as 0^0 is actually (0tending)^(0 tending). Log in or Sign up log in sign up. share. In the case of 1^∞, this value is undefined (since infinity doesn't appear in the real number system), and also indeterminate. Also need help finding the volume please. Can science prove things that aren't repeatable? when we say 1^infinity is indeterminate, its not exactly 1 in the base and not exactlt infinity in the power (infinity is not a number). You can sign in to vote the answer. However, you can use bad algebra or the Riemann Zeta function to assign the value of -1/12 to the series. You’re the manager of the Hilbert Grand Hotel. 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. What we mean is the base is approaching 1 (not 1 but very close to 1) and the power is approaching towards infinity (very large) Even after searching around, I can't come across a fairly understandable explanation. Why is 1^infinity indeterminate? As our story begins, you have a guest in every room. The problem is, we can't know for sure, since infinity is something we can't be sure about. This does not mean that the function itself is undefined at that point: for instance the function 0^0 is indeterminate, because (x→0, y→0)lim x^y may take on any value depending on the functions x and y, but it is not undefined (0^0 is defined to be 1). New comments cannot be posted and votes cannot be cast, More posts from the explainlikeimfive community. 2. To evaluate 1^infinity, infinity would need to be finite which it isn't by definition. Press question mark to learn the rest of the keyboard shortcuts. It has a countably infinite number of rooms, numbered from 1 upward. It has to do with the limit. Exponentiation is defined as repeated multiplication by the number. Indeterminate in this context means that the limit of a function cannot be determined by simply evaluting the function at the limit of its inputs. Your lack of understanding of what an indeterminate form makes me think that you shouldn't be so confident to call a well-established area of mathematics bogus. This is what 'infinity' is, and notions of 'unbounded quantities' need to be avoided for rigor, even though they may be conceptually understandable. The point is, it will take you an infinite amount of time to find out what 1^infty is; however, the trend states that 1^infty goes to 1. then 1^∞ = exp{0 • ∞) and 0 • ∞ is indeterminate. it's indeterminate since infinity stands for an unbounded limit not a number so 1^infinity is indeterminate. Saying that 1 ∞ is an indeterminate form is just a mnemonic way to say that you cannot compute lim x → c f (x) g (x) just by saying “the base goes to 1, so the limit is 1 because 1 t = 1 ”. Why is one to the power of infinity indeterminate??? This limit -- ##\lim_{n \to \infty}(1 + \frac 1 n)^n## -- is an example of this indeterminate form.