X^(n-1) = 0, what does x equal ?

1. May 11, 2006

meee

tnx

tnxtnxtnxtnx

Last edited: May 11, 2006
2. May 11, 2006

matt grime

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

3. May 11, 2006

meee

but its a^b = 0
soz, n is a natural number

4. May 11, 2006

rhj23

matt wouldn't have said that unless it applied to your problem.

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

5. May 11, 2006

meee

not that i know of? pls explian

Last edited: May 11, 2006
6. May 11, 2006

matt grime

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

7. May 11, 2006

meee

x*x m times

x^2 = xx
x^3 = xxx
x^m = x.....?

8. May 11, 2006

matt grime

So you do know how to make a power of x into a product of two (or more) numbers, all of which are x. Now, apply the first thing I posted.

9. May 11, 2006

meee

x^(n-1) = 0

x*x*x*x = 0?

10. May 11, 2006

matt grime

If you multiply any collection of (real) numbers together and get zero one of them must be zero, that is an underlying and very important fact about them, it is how you factor polynomials, remember?

11. May 11, 2006

meee

oh yeah... thanks :)

12. May 11, 2006

HallsofIvy

There are actually two answers to your question. For some values of n,
x= ___ . For other values of n, there is no such x.

13. May 11, 2006

AlphaNumeric

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.

14. May 11, 2006

matt grime

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.

Last edited: May 11, 2006
15. May 12, 2006

matt grime

Now I'm having second thoughts. A PID has no zero divisors because it is required to be an integral domain as well. Domain being, apparently, synonymous with integral domain, though that isn't necessarily universal: are domains presumed commutative?

16. May 12, 2006