Question about the differential in Calculus.

Assume a function y = f(x) , differentiable everywhere. Now we have for some Δx

Δy = f(x + Δx) – f(x)

The differential of x, is defined as “dx”, can be any real number, and dx = Δx

The differential of y, is defined by “dy” and

dy = f’(x) dx

Clearly,

Δy ≈ dy, depending on the magnitude of Δx.

In calculus an expression like “dx” usually denotes something infinitesimally small.

Why is it necessary to have dy and dx used as real numbers of some magnitude? In specifying and solving calculus problems are not the usual symbols sufficient?

Is it just a matter of notational convenience?