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Ok, I have been trying to figure this out, and even made a small program to try to figure it out, but after hours of running it and not finding anything that seemed to be "finished" I'll ask here...

How many triples of real numbers(x,y,z) are there such that xy=z, xz=y, and yz=x?

Are there any? Since z/y = y/z, mustn't z = y? Therefore, if my assumptions are correct, z/y and y/z would equal 1, which would then be x. However, zy can't then be x, can it?

(1,1,1) I think

hmmm....1,1,1 does seem to be it...with their being only 1 solution...

*cough*

(1, -1, -1)
(-1, 1, -1)
(-1, -1, 1)

Proof that these are all is fairly easy. For each of them, the magnitude must be equal to the magnitude of the two others multiplied -> the magnitude must be one for each. The direction for two must be either positive, different or negative, with a positive, negative or positive result (respectively). So, taking both positive gives a third positive, taking the first negative gives another negative, taking the second negative also gives another negative, taking both negative gives another positive. Four possibilities.

and 0, 0, 0? (not a real number?)

0 is not a real numer, nor is -1. real numbers range from 1 - inf.

This is of course assuming that i understand the meaning of the work "real" correctly. In danish i would discribe it asw natural numbers.

In English they are also natural numbers.

Real numbers are numbers which do not contain a complex component (no imaginary part).

N -- the set of natural numbers (0, 1,2,3,4,5,6..)
Z -- the set of integers (-4,-3,-2,-1,0,1,2,3,4...)
W -- the set of rational numbers (1/3, 2/3, 1/4, 2/5, 6.0, 5.0 etc)
R -- the set of all real numbers. (1.123141233..., 3.1415926535..., 7, 5,...)
C -- the set of all complex numbers (3, 5, 4, 4.34, 3+4i, 3+7i, etc...)

Going down the list each is a superset of the last.

Zacariaz wrote:0 is not a real numer, nor is -1. real numbers range from 1 - inf.

Real numbers are the numbers between -inf and +inf without imaginary parts. For each number in the real number set, there's an infinite number of real numbers between. Real numbers contain all rational numbers Q (any number from Z divided by any number from Z not equal to 0) and all the numbers between them that are not rational.

-1 and 1 are in Z (1 is in N, N union -N = Z)
So, -1/1 ( = -1) is in Q, so it is in R.

Dammit I put the rationals down as 'W' not 'Q'

JamesM wrote:Dammit I put the rationals down as 'W' not 'Q'

Wikipedia says I'm right

Candy wrote:

JamesM wrote:Dammit I put the rationals down as 'W' not 'Q'

Wikipedia says I'm right

ps. ik ben een beetje melig