What does it mean that the product of two vectors produces real number?

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I am going over inner product space.

I know that linear space has an inner product as long as it satisfies $4$ conditions.

And, the book says that for $x,y$ in $V$, there is a real number corresponding $(x,y)$

What does that mean?

For $\mathbb R^2$, where $x=(x_1,x_2)$, $y=(y_1,y_2)$, what is inner product of $(x,y)$, would it be $x_1y_1+x_2y_2$?