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## Main Question or Discussion Point

**tnx**

tnxtnxtnxtnx

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tnxtnxtnxtnx

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matt grime

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In the reals ab=0 if and only if one of a or b is zero.

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but its a^b = 0

soz, n is a natural number

soz, n is a natural number

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is there any way of writing your problem in the form a.b=0?

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not that i know of? pls explian

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matt grime

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What does x^m mean? (For m a natural number)

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x*x m times

x^2 = xx

x^3 = xxx

x^m = x.....?

x^2 = xx

x^3 = xxx

x^m = x.....?

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matt grime

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x^(n-1) = 0

x*x*x*x = 0?

x*x*x*x = 0?

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matt grime

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oh yeah... thanks :)

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HallsofIvy

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x= ___ . For other values of n, there is no such x.

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Somewhat unrelated, but that's because the Reals are a principle ideal domain isn't it? I'm vaguely trying to remember my 'Groups, Rings and Modules' course from 2 years ago.matt grime said:In the reals ab=0 if and only if one of a or b is zero.

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matt grime

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No. A principal ideal is one in which any ideal is generated by a single element. The reals, being a field, only have trivial ideals anyway (ie 0 and R). This has nothing to do with zero divisors. You're thinking of an integral domain. There are non principle ideal domains that are integral (eg Z[x,y]: the ideal (x,y) is not principle), and there are principal ideal domains that are not integral like Z/4Z.

As far as I'm concerned, the fact that there are no zero divisors in R comes first, therefore it implies they are an integral domain, rather than they are an integral domain therefore there are no zero divisors. Small point, and wholly semantic.

As far as I'm concerned, the fact that there are no zero divisors in R comes first, therefore it implies they are an integral domain, rather than they are an integral domain therefore there are no zero divisors. Small point, and wholly semantic.

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matt grime

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