$x + y = y + x$ is not a statement in Discrete Mathematics? I was reading my notes and i noticed something a little unusual. 
How is $$x + y = y + x$$ not a statement?
The reason that was given in the notes was "we don't know what $x$ and $y$ are, so they are not a statement. In Mathematics, $x$ and $y$ usually represent a real number."  
Mathematically, $x + y$ will always be the same as $y + x$ but why are they not considered as a statement?
Statement is a declarative statement that is either true or false but not both
 A: The expression $x+y=y+x$ is not a declarative statement that is either true or false. It becomes one (that happens to be true) if you insert specific real numbers for $x$ and $y$ (e.g., $3+\pi=\pi+3$), but as it stands, the symbols $x$ and $y$ do not represent specific real numbers. You might as well write $\square+\triangle=\triangle+\square$, with the understanding that the square and triangular boxes are ‘containers’ waiting to be filled with specific numbers.
You might suppose that it asserts that $x+y$ and $y+x$ are equal no matter what numbers you substitute for $x$ and $y$, but this isn’t how the notation works. If that’s what you want to say, you have to express the no matter what part explicitly:

$$\forall x\,\forall y\,(x+y=y+x)\;,$$

or 

for all real numbers $x$ and $y$, $x+y=y+x$.

This potential confusion arises because people, including writers of textbooks, are sometimes sloppy and omit the quantifying expression ($\forall x\,\forall y$ or for all real numbers $x$ and $y$) when they think that it can be reasonably understood from context.
A: Since it's not stated to apply for all $x$ and $y$, only some unknown particular $x$ and $y$, it declares nothing about the commutativity of addition nor about the properties of your equals sign.  And if you know the properties of your equals sign and addition operator then it's not a statement because it declares nothing about $x$ and $y$.
But I think it is a statement under certain circumstances, for example if your addition was not known to be commutative in general then this statement declares that there is some pair $x,y$ such that addition does commute.
The intended statement is probably:
$$x+y=y+x \space\forall (x,y)$$
Which correctly declares that your addition operator is commutative.
