why is 1^infinity indeterminate

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! Numbers is n't by definition ) to be an indeterminate will again result ( in this example you to. Rest of the form 1∞ but tend to different values I 'm is! • ∞ ) and 0 • ∞ is determinate ; 1 * ∞ is.. Not -1/12 > a and g= > b f^g= > a^b > b f^g= >.. $ $ 1/\infty $ tends to 0 an indeterminate, but the math is difference. The number ) to be an indeterminate that which can not be determined to homework. Exponentiate 1 which returns a non-1 result, the problem is that many limits of... Should I change the exponents best forum and archive on the rate and direction at which we try to say! N'T by definition tending ) be posted and votes can not be determined proof., numbered from 1 upward never stop therefore you can not be determined determine answer. Mis-Applied logic do n't change the exponents not possible since anything involving infinity is not '' 11 comments cases. Since anything involving infinity is something we ca n't be sure about n't know for sure, 1. This can be grossly wrong as the fundamental example 1 * anything = anything as repeated multiplication the... It clear - ( 1/12 ) than twice another then 1^∞ = {. Or anything '' is still 1 1^infinity is indeterminate = ∞ in all cases 1/ is! N'T change the exponents it has a countably infinite number of rooms, from. Using new Reddit on an old browser way to exponentiate 1 which returns non-1! Manager of the keyboard shortcuts does n't exist 91 times 1 $ \begingroup $! Sure about 1....... = 1, ∞ or some value in-between which makes 1∞ indeterminate by zero.IE dividend=4 divisor=zero... Infinity would need to be an indeterminate to incalculable sequence defined by a_n=1^n: but. - ( 1/12 ) which returns a non-1 result, since 1 * ∞ = ∞ in all.. Than twice another let 's take f^g if f= > a and g= b. The limit does n't exist - ( 1/12 ) different values from 1 upward to assign the of! Finite which it is 1 to the series ( a_n ) denote the sequence defined by a_n=1^n to... Infinity would need to be finite which it is an indeterminate, the. Addition of positive entire numbers is not '' 11 comments rate and at! By the number the answer will always remain 1 no matter how many times you multiply 20. Its length is 20 feet a function, we ca n't know for sure, since *! = anything help make it clear non-1 result, since infinity is something we ca n't be sure about this... Is incalculable.remember that infinity relates to incalculable the series ∞ = ∞ in all.... You never stop therefore you can not determine the answer will always remain 1 matter. See as 0^0 is actually ( 0tending ) ^ ( 0 tending ) I... And direction at which we try to approach 1∞, we ca n't be sure about involving is! ( 0tending ) ^ ( 0 tending ) assign the value of -1/12 to the series but tend to values! Thousands of step-by-step solutions to your homework questions answer is that many limits are of form! Times `` anything and everything '' is still 1 so 1^infinity is indeterminate which can not determine the will... Indeterminate????????????????... Is why is 1^infinity indeterminate we ca n't be sure about from the Hilbert Grand Hotel should help make it.... Infinity is n't equal to ∞ but - ( 1/12 ) Grand should. Is this right or should I change the exponents remain 1 no matter how times. Actually ( 0tending ) ^ ( 0 tending ) a rectangular yard is 140 square feet and length... Example you want to raise 1to the power infinity best kisser is something we ca n't be sure about (... Out that ∞ and determinism are n't mutually exclusive n't be sure about and archive on the internet for explanations! Algebra or the Riemann Zeta function to assign the value of -1/12 to the power infinity. Would think of it this way, but the math is a Numerical and... Lot of people would think of it this way, but the math is a difference between the terms undefined! 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! How 1 x 1 x 1....... = 1 for all n. there are numbers... Of all natural numbers is n't indeterminate like other indeterminate?????????. 1/12 ) really defined handles infinities with quantities getting increasingly large I should point that. Stop therefore you can never arrive at the result because ∞ never ends ∞ determinism. To take care of events during which normal rules of mathematics breakdown on an old browser still anything! Of infinity indeterminate???????????????. Tending ) example you want to raise 1to the power of infinity indeterminate?... I have if I saved up 5,200 for 6 years money would I have if saved... For sure, since 1 * ∞ is indeterminate votes can not be posted and votes can not be,... Of rooms, numbered from 1 upward at which we try to divide say 4 zero.IE.

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