Is the function notation deprecated?

From WolframAlpha: http://mathworld.wolfram.com/Function.html "While this notation is deprecated by professional mathematicians, it is the more familiar on开发者_高级运维e 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?

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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.