Did I pick the error? Mathematical Logic Given these propositions:
$$\begin{align}
x&amp;=y \\
x^2&amp;=xy \\
x^2-y^2&amp;=xy-y^2\\
x+y&amp;=y\\
y+y&amp;=y\\
2y&amp;=y\\
2&amp;=1
\end{align}
$$
I've found out that the error is "$x+y=y$". Am I correct? I'm just a beginner in Discrete Math.
Um, sort of? It's supposed to be factoring both sides of the equation into

$$(x-y)(x+y)=(x-y)y$$

and dividing by $x-y$ to yield

$$x+y=y$$

which seems fine at first glance. But the problem is when you divide by $x-y$ you're actually dividing by $0$ because $x=y$.
The fish rots from the head: $x=y\Leftrightarrow x^2=xy$ holds iff $x\neq0$.