Question

From WolframAlpha: http://mathworld.wolfram.com/Function.html
“While this notation is deprecated by professional mathematicians, it is the more familiar one for most nonprofessionals. Therefore, unless indicated otherwise by context, the notation is taken in this work to be a shorthand for the more rigorous .”

Referring to f(x) being deprecated in favor of f:x->f(x).

I thought this was interesting because I’ve been familiar with:

 function name(arg)

In all my years of middle school through high school, I have never seen functions with any other notation, what is the benefit of using f:x->f(x) instead of f(x)? If f(x) really is deprecated, why do programming languages continue to use a similar syntax?

Answer 1

You’re taking the quote out of context. The page says “However, especially in more introductory texts, the notation f(x) is commonly used to refer to the function f itself (as opposed to the value of the function evaluated at x). In this context, the argument x is considered to be a dummy variable whose presence indicates that the function f takes a single argument (as opposed to f(x,y), etc.)” and then says that that’s what deprecated.

In most programming languages f(x) refers to the function f evaluated with the argument x and writing f(x) when x is not defined is an error. So they don’t use f(x) in its deprecated sense.

To refer to the function f itself, you’d use just f or lambda x: f(x) or something similar depending on the programming language.