2 Ded3 D3 F E566 4 D89 9032 42 Fdf5806 Ef4 Hosted At Imgbb Imgbb The product of 0 and anything is $0$, and seems like it would be reasonable to assume that $0! = 0$. i'm perplexed as to why i have to account for this condition in my factorial function (trying to learn haskell). It is possible to interpret such expressions in many ways that can make sense. the question is, what properties do we want such an interpretation to have? $0^i = 0$ is a good choice, and maybe the only choice that makes concrete sense, since it follows the convention $0^x = 0$. on the other hand, $0^ { 1} = 0$ is clearly false (well, almost —see the discussion on goblin's answer), and $0^0=0.
Eb88711 D Bdf3 4 F6 B 9 Ea0 1 F2 Bbcbb6303 Postimages Is a constant raised to the power of infinity indeterminate? i am just curious. say, for instance, is $0^\\infty$ indeterminate? or is it only 1 raised to the infinity that is?. Is there a consensus in the mathematical community, or some accepted authority, to determine whether zero should be classified as a natural number? it seems as though formerly $0$ was considered i. In the set of real numbers, there is no negative zero. however, can you please verify if and why this is so? is zero inherently "neutral"?. In the context of limits, $0 0$ is an indeterminate form (limit could be anything) while $1 0$ is not (limit either doesn't exist or is $\pm\infty$). this is a pretty reasonable way to think about why it is that $0 0$ is indeterminate and $1 0$ is not. however, as algebraic expressions, neither is defined. division requires multiplying by a multiplicative inverse, and $0$ doesn't have one.
343420 Ac Ea87 4 B9 C 9973 55 Dfe96 B8 C5 A Hosted At Imgbb Imgbb In the set of real numbers, there is no negative zero. however, can you please verify if and why this is so? is zero inherently "neutral"?. In the context of limits, $0 0$ is an indeterminate form (limit could be anything) while $1 0$ is not (limit either doesn't exist or is $\pm\infty$). this is a pretty reasonable way to think about why it is that $0 0$ is indeterminate and $1 0$ is not. however, as algebraic expressions, neither is defined. division requires multiplying by a multiplicative inverse, and $0$ doesn't have one. Why is any number (other than zero) to the power of zero equal to one? please include in your answer an explanation of why $0^0$ should be undefined. @swivel but 0 does equal 0. even under ieee 754. the only reason ieee 754 makes a distinction between 0 and 0 at all is because of underflow, and for ∞, overflow. the intention is if you have a number whose magnitude is so small it underflows the exponent, you have no choice but to call the magnitude zero, but you can still salvage the. I began by assuming that $\dfrac00$ does equal $1$ and then was eventually able to deduce that, based upon my assumption (which as we know was false) $0=1$. as this is clearly false and if all the steps in my proof were logically valid, the conclusion then is that my only assumption (that $\dfrac00=1$) must be false. But: i know what i am writing about. i have a phd mathematics, and have seen all these arguments by people who let $0^0$ undefined, and i have seen even more arguments by people who define $0^0=1$ and these arguments have convinced me. and probably they will also convince you once you open yourself to them. think before downvoting!.
87207 B33 Dff3 4 Ec0 A61 D 02406 E65 F73 B Hosted At Imgbb Imgbb Why is any number (other than zero) to the power of zero equal to one? please include in your answer an explanation of why $0^0$ should be undefined. @swivel but 0 does equal 0. even under ieee 754. the only reason ieee 754 makes a distinction between 0 and 0 at all is because of underflow, and for ∞, overflow. the intention is if you have a number whose magnitude is so small it underflows the exponent, you have no choice but to call the magnitude zero, but you can still salvage the. I began by assuming that $\dfrac00$ does equal $1$ and then was eventually able to deduce that, based upon my assumption (which as we know was false) $0=1$. as this is clearly false and if all the steps in my proof were logically valid, the conclusion then is that my only assumption (that $\dfrac00=1$) must be false. But: i know what i am writing about. i have a phd mathematics, and have seen all these arguments by people who let $0^0$ undefined, and i have seen even more arguments by people who define $0^0=1$ and these arguments have convinced me. and probably they will also convince you once you open yourself to them. think before downvoting!.
6594328 E 5 B0 F 4 C7 F 82 B0 D0 D5 D1957010 Hosted At Imgbb Imgbb I began by assuming that $\dfrac00$ does equal $1$ and then was eventually able to deduce that, based upon my assumption (which as we know was false) $0=1$. as this is clearly false and if all the steps in my proof were logically valid, the conclusion then is that my only assumption (that $\dfrac00=1$) must be false. But: i know what i am writing about. i have a phd mathematics, and have seen all these arguments by people who let $0^0$ undefined, and i have seen even more arguments by people who define $0^0=1$ and these arguments have convinced me. and probably they will also convince you once you open yourself to them. think before downvoting!.
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