Is the following a total function, a partial function or total, single-valued relation?
$h: \mathbb{N} \rightarrow \mathbb{N}$, where $h(n) = \Bigg\{0 $ if $n$ is divisible by $2$, $1$ if $n$ is divisible by $3$, $2$ otherwise
My thought is that this is just a total, single-valued relation, since every element in the natural numbers is mapped to one of the three (0, 1 and 2), however, it is not single valued - for example every even number will be mapped to 0, every multiple of three will be mapped to 1 and everything else will be mapped to 2.
Sorry in advance for the poor formatting