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Why operation * not defined in Q

by pakkanen
Tags: defined, operation
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pakkanen
#1
Jan24-13, 10:44 AM
P: 12
1. The problem statement, all variables and given/known data

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 *?
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jbunniii
#2
Jan24-13, 10:47 AM
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Quote Quote by pakkanen View Post
1. The problem statement, all variables and given/known data

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 [itex]l[/itex] and [itex]m[/itex]?
pakkanen
#3
Jan24-13, 12:04 PM
P: 12
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
#4
Jan24-13, 12:25 PM
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Why operation * not defined in Q

Quote Quote by pakkanen View Post
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
#5
Jan24-13, 01:07 PM
P: 12
Thank you very much jbunniii! Helped me a lot. I think we'll meet again.


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