# Notation for domains

## Main Question or Discussion Point

If you have an equation with a variable which isn't defined for a given value or values, how do you express this in proper notation? For example:
x=1/((y-2)(y-3))

Do I write simply " y<2 or 2<y<3 or 3<y" or is there a better way to express it?
Thx

arildno
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If you have an equation with a variable which isn't defined for a given value or values, how do you express this in proper notation? For example:
x=1/((y-2)(y-3))

Do I write simply " y<2 or 2<y<3 or 3<y" or is there a better way to express it?
Thx
There exist no strictly better ways than the one you've chosen, but it is perhaps slightly more conventional to use standard set notation. your "or" is then replaced by the symbol for "union" (a "U"), and your (strict) inequalities are replaced by indicating the open sets the inequality indicates.
For example, we may write yours that "y" is an element of:
(-inf,2)U(2,3)U(3,inf)

Alternatively, we might write something like:
$$y\in\mathcal{R},y\neq{2},y\neq{3}$$

Again, your own expression is perfectly fine.