# Is there a generally accepted name for the function $f = \{0 \text{ when } x=0, 1 \text{ when } x ≠0 \}$?

In one of my computer programming projects I have defined the following quite common function:

$$f(x) = \begin{cases} 0, & \text{ when } x = 0, \\ 1, & \text{ when } x \neq 0. \end{cases}$$

From what I understand, this is essentially an indicator function, more specifically $1_{x \neq 0}$. Unfortunately, most programming languages are quite restrictive in what one can use as an indentifier and mathematical symbols do not generally make the cut.

So, is there a standard name for this function? Something familiar to English-speaking$^1$ scientists that could be used in computer code$^2$?

$^1$ Yes, that means that something in, say, Sanskrit or Chinese would not be of much help.

$^2$ functionThatReturnsZeroForZeroInputAndOneOtherwise is not very helpful either...

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Yes, Kronecker delta, or Characteristic function, or Indicator function, as you said. – Berci Feb 3 '13 at 14:01
actually, this would be one minus the Kronecker delta. – J. Loreaux Feb 3 '13 at 14:03
Indeed, $x\mapsto 1-\delta_{0,x}$. In the theory of Boolean algebras (with operators), this is called the switching function or discriminator (though it means some more general thing in universal algebra). – Berci Feb 3 '13 at 14:05
But, overall, I would call it simply NonZero(x). – Berci Feb 3 '13 at 14:08
@Berci: to be honest I was hoping for a name that would not be confused with a function that returns a boolean value. Something along the lines of nonZeroIndicator() or something... – thkala Feb 4 '13 at 10:31

You might call it normalize () or canonicalize (), since it normalizes/canonicalizes a representation in which false / $0$ is represented by $0$ and true / $1$ can be represented by any non-zero value to a representation in which each of them is represented by only one "canonical" value, which can then be used e.g. in equality comparisons.