The discussion revolves around the operation defined as l/m * k/n = (l+k)/(m²+n²) and its validity within the set of rational numbers Q, where l and k are integers, and m and n are non-zero integers. Participants are exploring why this operation cannot be consistently defined in Q.
Some participants have noted that the operation appears to produce different outcomes, suggesting that it may not be well-defined. There is an acknowledgment of the need to clarify the implications of negating variables within the operation.
Participants are considering the constraints of the operation and its definitions within the context of rational numbers, particularly the implications of using integers and non-zero denominators.
pakkanen said: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 *?
That's right, so the operation is not well defined.pakkanen said: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