assignments/week1/1.tex

@@ -204,13 +204,14 @@ See the assignment PDF for the full assignment specification and theorem.
                     \frac{x_1*x_1}{p_1***p_N*q_1***q_M} &= \frac{x_2*x_2}{v_1***v_n*w_1***w_m}
                 \end{align}
 
-                I'm kinda stuck at this point. I see that this is definitely injective, since the way the exponents
+                \textit{I'm kinda stuck at this point.
+                I see that this is definitely injective, since the way the exponents
                 are defined, you will always know which prime factors belong to the numerator or to the denominator.
                 But I fail to prove this using the direct definition of $f$ like we could do for the natural numbers.
                 This is because the products of the denominators in the last equation are not unique.
                 So maybe I simplified them too much and shouldn't try and write them in terms of $x_1$ and $x_2$ like
                 we did earlier, and try and focus more on just the exponents, but I feel it becomes really hard
-                to show that $x_1 = x_2$ that way.
+                to show that $x_1 = x_2$ that way.}
 
             \item[Surjectivity:] We want to show that $f$ is onto, i.e. $f(\{ q > 0 : q \in \Q \}) = \N$.