Why operation * not defined in Q

[pakkanen]

Homework Statement

Show that l/m * k/n = (l+k)/(m²+n²) can not be defined as an operation in Q when l,k € Z and m, n € Z\{0}

I do not know what is the issue here? Should I know something about Q that this not fulfilled by the operation *?

 

[jbunniii]

Homework Statement

Show that l/m * k/n = (l+k)/(m²+n²) can not be defined as an operation in Q when l,k € Z and m, n € Z\{0}

I do not know what is the issue here? Should I know something about Q that this not fulfilled by the operation *?

Hint: What happens if you negate $l$ and $m$?

 

[pakkanen]

Ok.. So the same operation can produce two different results??

So that l/m * k/n = (l+k)/(m2+n2) ≠ (-l+k)/((-m)²+n²) = -l/-m * k/n = l/m * k/n

 

[jbunniii]

Ok.. So the same operation can produce two different results??

So that l/m * k/n = (l+k)/(m2+n2) ≠ (-l+k)/((-m)²+n²) = -l/-m * k/n = l/m * k/n

That's right, so the operation is not well defined.

 

[pakkanen]

Thank you very much jbunniii! Helped me a lot. I think we'll meet again.