Let's say we live in a world where we have the technology to simulate 4-dimensional graphs with 3-dimensional vision. What will be the variable representing the fourth dimension? We already used x, y, and z to represent the 3 dimensions. There is no letter after z in the latin alphabet.
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1At a certain point people begin to use subscripts, e.g., $(x_1,x_2,x_3,x_4)$. But $(x,y,z,w)$ is also not uncommon. – kccu Dec 31 '16 at 02:48
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It really can be whatever you want. Hell, I can make the assignment $(x, y, z) = (w, q, $\lambda)$, even if it's silly. – Sean Roberson Dec 31 '16 at 02:56
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The naming of variables is inessential.
This is a general truth in all of mathematics. Go ahead and choose $(n,\kappa,!,\aleph)$, if you wish to do so. In any case, here is another truth that has equal importance:
You should strive not to confuse the reader/listener.
Therefore it is best not to make choices that are as wild as the extreme example above for your symbols. This is why most real analysis texts keep using the standard $x$ for the real variable$^{(\star)}$, or $(x,y)$ for the variable in $\mathbb R^2$. The common choice for four components, specifically one that readily bypasses the issue you're mentioning, is $(x_1,x_2,x_3,x_4)$.
$^{(\star)}$ Though, for example, I know of a professor at my university that used to teach the whole course with $\lambda$'s instead of $x$'s. That drove students crazy, much to his pleasure — I guess he managed to make his point.
giobrach
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