## Is it just me not understanding some implicit rules or most of definitions of functions appearing in literature are ambiguous (in part. in physics)? I’m especially interested in the ambiguity of the sign of equality (see the explanations below) i.e. is it really ambiguous or I don’t understand something?

The following definition of a function seem ambiguous, at least to me: y = 5; it is because the definition neither explicitly says nor implies that it is dependent on some variable. I admit that normally such a definition is given in a context e.g. x and y axes, etc. However, even then one still can argue that y = 5 is not dependent on x and merely represents one point at mark 5 on the y axis. The given example is maybe to trivial to explain the ambiguity. Let’s concern a function in R^2 which is given as follows f = < 2t, sin(t) >. The assumption is that it is a vector function in 2D which depends only on t (i.e. f(t) = = < 2t, sin(t) >) and therefore represents a curve (a set of points in 2D). However, as dependencies are not indicated, it also can be that it depends on further variables e.g. on x, y and t, which means that the function f(x,y,t), for instance, represents a time dependent, 2D vector field (an infinite set of vectors for each given t). Equally, t may be not a parameter but one of two space coordinates i.e. f(t,u) which means that it represents a constant, 2D vector field (an infinite set of vectors). Furthermore, the very sign of equality when “defining” functions may be ambiguous. Consider a generalised position vector in R^3 e.g. **r** = < x,y,z >. When I say **g** = **r** do I define a vector field **g** or do I simply define another position vector **g**? To my taste **g**(**r**) = **r** would rather indicate definition of the vector field, whereas **g** = **r** would rather define another position vector. Or maybe, for some obscure reason, it is assumed that only one “generalised” position vector (“the” infinite set of vectors pointing from the origin to all possible locations in R^3) may exist so if you define **r** as a generalised position vector, each time you say e.g. **u** = **r** you automatically define a vector filed?