# What does the semicolon ; mean in a function definition

Cauchy's Hypothesis or Noll's theorem states that $\vec{t}(\vec{X},t;\partial \Omega) = \vec{t}(\vec{X},t;\vec{N})$ where $\vec{N}$ is the outward unity normal to the positively oriented surface $\partial \Omega$. This translates to words as the dependence of the surface interaction vector on the surface on which it acts is only through the normal $\vec{N}$. My question is what is the significance of the semicolon (;)? How does it differ from the comma (,) used to separated the function's first two arguments?

A semicolon is used to separate variables from parameters. Quite often, the terms variables and parameters are used interchangeably, but with a semicolon the meaning is that we are defining a function of the parameters that returns a function of the variables.

For example, if I write $$f(x1,x2,\ldots;p1,p2,\ldots)$$ then I mean that by supplying the parameters $$(p1, p2,\ldots)$$, I create a new function whose arguments are $$(x1, x2,\ldots)$$.

So the general syntax is $$\operatorname{functionName}(\mathrm{variables};\mathrm{parameters})$$.

In Noll's theorem it says that the function created by supplying $$\partial \Omega$$ is the same as that created by supplying $$\vec{N}$$. That's rather a nice way of saying that the function created only depends on $$\vec{N}$$.

• I was still a little confused by the answer until I read mathsisfun.com/definitions/parameter.html Dec 3, 2017 at 11:37
• In programming terms, parameter is a name for a variable in function definition. When using the function, you give arguments. I tend to think that the general syntax in math is funcname(variable parameters; fixed parameters). You need both to calculate the return value for the function, but the second set is usually fixed.
– np8
Dec 2, 2020 at 15:52

There is no hard mathematical difference between the comma (,) and the semicolon(;).

The semicolon is used sometimes to optically separate some variable group. So the semicolon is not more than a reading aid.

The situation can be compared to the usage of different kind of parentheses, to make complex nestings more readable.