Proper notation for a point
If a point $P$ is assigned an ordered pair $(x, y)$ is it better notation to write $P(x, y)$ or since $P$ is uniquely assigned the ordered pair to write $P \equiv (x, y)$ (or even $P = (x, y)$ to cover all bases)?
$\endgroup$ 41 Answer
$\begingroup$The traditional notation, given the axes, is to write $P$ $(x,y)$ in diagrams. Note the space between the $P$ and the $(x,y)$. The meaning is that $x$ and $y$ are the coordinates (note the plural) assigned to $P$. Over time, $(x,y)$ has become identified with a single object: a vector of these coordinates. Thus, while it is not strictly correct to say that $P$ is $(x,y)$, the identification doesn't matter as long as only one coordinate system is being used.
Using the notation $P(x,y)$ is rather a muddle; it seems to be implying that $P$ is a function of $x$ and $y$. Your suggestion of using another sign, such as $\equiv$, to show the correspondence between $P$ and $(x,y)$ is reasonable, but I don't think it has much currency. We are rather stuck with the often miswritten $P$ $(x,y)$ for the present, until a better convention becomes established.
$\endgroup$
