# Injection on QxQ

For the set {a^2+b^2 , a,b $\in$ Q}. Am i then right in saying that the map:

f(a^2+b^2)=(lal,lbl) is an injection on QxQ (the absolute values are there to make sure f is well-defined)? And is this how you write a thing like this formally.

Office_Shredder
Staff Emeritus
Gold Member
Your function is not well defined - note that a2+b2 is always an element of Q if a and b are, so you are saying f(x) = (|a|,|b|) for any way that I can pick a and b to write x = a2+b2. There are generally going to be multiple ways to write x in this way, for example
4 = 02 + 22 = 22 + 02,

so is f(4) supposed to be (2,0) or (0,2)?

ugh I see I made a mistake:
What I meant was:
f(a^2+b^2)=lal+lbl
now f is injective right?