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The product of 0 and anything is $0$, and seems like it would be reasonable to assume that $0! In the set of real numbers, there is no negative zero. However, can you please verify if and why this is so? I heartily disagree with your first sentence. Is there a consensus in the mathematical community, or some accepted authority,.

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In the set of real numbers, there is no negative zero. The reason $0/0$ is undefined is that it is impossible to define it to be equal to any real number while obeying the familiar algebraic properties of the reals. Or is it only 1 raised to the infinity that is? Is a constant raised to the power of infinity.

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The question is, what properties do we want such an interpretation to have? 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 $\pm\infty$). Is there a consensus in the mathematical community, or some accepted authority, to determine whether zero should be classified as a natural.

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The reason $0/0$ is undefined is that it is impossible to define it to be equal to any real number while obeying the familiar algebraic properties of the reals. In the set of real numbers, there is no negative zero. It is possible to interpret such expressions in many ways that can make sense. Say, for instance, is $0^\\infty$ indeterminate?.

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$0^i = 0$ is a good. Say, for instance, is $0^\\infty$ indeterminate? Or is it only 1 raised to the infinity that is? In the set of real numbers, there is no negative zero. Please include in your answer an explanation of why $0^0$ should be undefined.

0 Down Car Deals - I heartily disagree with your first sentence. It seems as though formerly $0$ was. $0^i = 0$ is a good. In the set of real numbers, there is no negative zero. Is there a consensus in the mathematical community, or some accepted authority, to determine whether zero should be classified as a natural number? However, can you please verify if and why this is so?

In the set of real numbers, there is no negative zero. Please include in your answer an explanation of why $0^0$ should be undefined. Or is it only 1 raised to the infinity that is? $0^i = 0$ is a good. I heartily disagree with your first sentence.

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This is a pretty reasonable way to. $0^i = 0$ is a good. Say, for instance, is $0^\\infty$ indeterminate? Is a constant raised to the power of infinity indeterminate?

There's The Binomial Theorem (Which You Find Too Weak), And There's Power Series And Polynomials (See Also Gadi's Answer).

I heartily disagree with your first sentence. The question is, what properties do we want such an interpretation to have? 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 $\pm\infty$). However, can you please verify if and why this is so?

The Product Of 0 And Anything Is $0$, And Seems Like It Would Be Reasonable To Assume That $0!

Is there a consensus in the mathematical community, or some accepted authority, to determine whether zero should be classified as a natural number? Or is it only 1 raised to the infinity that is? The reason $0/0$ is undefined is that it is impossible to define it to be equal to any real number while obeying the familiar algebraic properties of the reals. In the set of real numbers, there is no negative zero.

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. It is possible to interpret such expressions in many ways that can make sense. It seems as though formerly $0$ was.