Using a semicolon in a functin argument. eg. f = f(x, y; t)

[mikeph]

Hi
I've seen this a few times, where we say f = f(x, y; t) for example, without a proper definition or any guidelines of usage. In my mind I read this as "f is a function over x and y, but it is also dependent on t although this is usually a fixed parameter", even though we might have some function like

f(x,y;t) = yx²/t

i.e. from looking at the form of f, you could not tell which variables would go either side of the semicolon.

Perhaps it can also be read as f being a family of functions over (x,y), where each is parametrised by t. But then this is just semantics, the maths is no different, so what's the point in the semicolon?

Does anyone know a better definition of this notation?

Thanks
Mike

 

[jedishrfu]

I think its your second definition of a set of surfaces in 3-space with varying 't' value.

 

[jbunniii]

Perhaps it can also be read as f being a family of functions over (x,y), where each is parametrised by t. But then this is just semantics, the maths is no different, so what's the point in the semicolon?

There is no mathematical need for the semicolon. The notations $f(x,y;t)$ and $f(x,y,t)$ mean the same thing. The semicolon is there because the author wants to group the function parameters in some way, hopefully for the convenience of the reader: perhaps $x$ and $y$ are spatial coordinates and $t$ is time.

 

[mikeph]

Ah, perfect. That is exactly what I want to do.

Thanks!

 

[CellCoree]

Hello Mike,

Thank you for bringing up this topic. The usage of semicolons in function arguments can be a bit confusing and there are varying opinions on its proper use. In general, the semicolon is used to indicate a separation between independent and dependent variables in a function. So in the example f = f(x, y; t), the semicolon is indicating that t is a dependent variable while x and y are independent variables.

Some mathematicians argue that the semicolon should be used when there is a clear distinction between independent and dependent variables, while others argue that it should only be used when there is a specific reason for doing so. In the end, it comes down to personal preference and the specific context in which the function is being used.

In the case of f(x,y;t) = yx2/t, I would argue that the semicolon is not necessary as the function is clear and the variables are all related in a straightforward manner. However, in more complex functions where there may be a mix of independent and dependent variables, the semicolon can help to clarify the relationship between them.

Ultimately, the use of the semicolon in function arguments should be consistent within a particular context or field of study. If there is no clear consensus on its usage, it may be best to avoid it altogether and find alternative ways to indicate the relationship between variables. I hope this helps to clarify the issue.