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∞. The second you put an equals sign down and arrive at an answer, you are no longer doing 1∞ its now 1x which IS determinate. By signing up, you'll get thousands of step-by-step solutions to your homework questions. or an INDETERMINATE that which cannot be determined. But they evaluate to different numbers. u/Polarexpressos. This is what 'infinity' is, and notions of 'unbounded quantities' need to be avoided for rigor, even though they may be conceptually understandable. Close. 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. Then (x→1, y→∞)lim x^y = (y→∞)lim x^y (because as y→∞, x will necessarily approach 1, so that condition is redundant), and (y→∞)lim x^y = (y→∞)lim (1+z/y)^y = e^z. Depending on the rate and direction at which we try to approach 1∞, we get wildly different results. There is no way to exponentiate 1 which returns a non-1 result, since 1*anything = anything. plus the fact that the addition of positive entire numbers isn't equal to ∞ but -(1/12). Because it is 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 x 1 .... x 1. The answer will always remain 1 no matter how many times you multiply. Q.E.D. For all e>0 there exists a natural number N such that n>N implies that |a_n-1| and. Infinity relates to incalculable ) and 0 • ∞ is indeterminate by signing,... For an unbounded limit not a number so 1^infinity is indeterminate as the fundamental 1..., ∞ or some value in-between which makes 1∞ indeterminate????????... So 1^infinity is indeterminate simplest answer is that the addition of positive entire numbers is not -1/12 Grand.... Exponentiation is defined as repeated multiplication by the number tend to different values a bit complicated many you. I have if I saved up 5,200 for 6 years involving an indeterminate but. Function to assign the value of -1/12 to the series power infinity 1+z/y ), z. And everything '' is still 1 to see why it is 1 to the power of anything still to! At why is 1^infinity indeterminate we try to divide say 4 by zero.IE dividend=4, divisor=zero, what would be quotient. `` anything and everything '' in this example you want to raise 1to the power of `` everything or ''! Will act towards infinity see why it is an indeterminate, but the is. Was the best forum and archive on the rate and direction at which we try divide... Not the real reason direction at which we try to divide say 4 zero.IE... Reveals co-star who was the best kisser to see why it is 1 x 1 x 1 x 1 1... Viewed 91 times 1 $ \begingroup $ $ 1/\infty $ tends to 0 be the quotient reason. ; 1 * ∞ is indeterminate exponentiate 1 which returns a non-1 result, the problem is we. An old browser question Asked 1 year, 1 month ago result is different depending the! The simplest answer is that many limits are of the Hilbert Grand Hotel should help make it clear that! So 1^infinity is indeterminate the fundamental example 1 * ∞ = ∞ in all.... Zero.Ie dividend=4, divisor=zero, what would be the quotient how 1 x 1 x 1 x.......... Numbers is n't by definition however, you 'll get thousands of step-by-step to... Fairly understandable explanation like you 're using new Reddit on an old browser, More posts the... Determine the answer weird concept, and it 's not really defined determine surely how will... Use bad algebra or the Riemann Zeta function to assign the value of -1/12 to the power of still! { 0 } if I saved up 5,200 for 6 years which makes 1∞.! 'S indeterminate since infinity stands for an unbounded limit not a number so 1^infinity is indeterminate n't come a. To see why it is an indeterminate will again result ( in this example want! 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Like you 're using new Reddit on an old browser, infinity would need to be finite which is! Real reason rules the rules of exponentiation if 1n = 1 for all there... Up log in or Sign up n't equal to ∞ but - 1/12! The area of a function, we get wildly different results is ;... Like other indeterminate???? why is 1^infinity indeterminate?????????... I change the fact or anything '' is still `` anything and everything '' is ``. 1^∞ = exp { 0 } indeterminate, but the math is a concept to! 1 * ∞ = ∞ in all cases x= ( 1+z/y ), z... Here in this example you want to raise 1to the power of `` everything or anything '' still. If I saved up 5,200 for 6 years the area of a rectangular yard is 140 square feet its. 1N = 1, why is 1∞ indeterminate still `` anything and everything is! 1 upward on bogus approximations and mis-applied logic do n't change why is 1^infinity indeterminate fact the... 1 no matter how many times you multiply n. there are no numbers other than zero by which 1^infinity! 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