# What is a “n-valued function”?

Has $$n$$ parameters?

i.e.

0-valued function: $$f(\emptyset)=2$$

1-valued function: $$f(x)=x$$

2-valued function: $$f(x,y)=x+y$$

3-valued function: $$f(x,y,z)=x+y+z$$

Not sure

• Pretty sure that "0/1-valued" means that the output is always 0 or 1. But context is everything, so please let us know where you found this. – Morgan Rodgers Mar 18 at 0:35
• Just the phrase "0/1-valued function" suggests that the function's codomain is the set $\{0,1\}$. – vadim123 Mar 18 at 0:36
• If I hear "n-valued function" I think the mean $f(x)$ may have multiple outputs (violating the standard definition of "function" which is practically writ in stone that a well-defined function has a single output for each point in the domain). For example $f:[-1,1]\to [0,2\pi)$ via $f(x) = \theta$ if $\sin \theta x$ is a 2-value "function". But in this context I really actually have no idea. – fleablood Mar 18 at 0:37
• "retty sure that "0/1-valued" means that the output is always 0 or 1." and "Just the phrase "0/1-valued function" suggests that the function's codomain is the set {0,1}". D'oh! That is almost certainly the case.... – fleablood Mar 18 at 0:37
• It's from a class on Theory of Computation, topic: Recursive and Recursively Enumerable Sets. "total" here means there's always an output (never undefined) so I think 1st commenter is right. – A_for_ Abacus Mar 18 at 0:40

$$\phi_x:{\Bbb N}_0^k\rightarrow {\Bbb N}_0$$ is a total 0/1-valued function means that the domain of $$\phi_x$$ is $${\Bbb N}_0^k$$ and the range is $$\phi({\Bbb N}_0^k)\subseteq \{0,1\}$$.