Hey all, i've come across a problem i'm stumped on:

Let S be the set of all functions u: N -> {0,1,2} Describe a set of countable functions from S

We're given that v1(n) = 1, if n = 1 and 2, if n =/= 1

The function above is piecewise, except i fail with latex

To begin with, im not exactly sure what the question is asking, are we looking for all functions u that map the natural numbers to either 0,1,2 since i imagine there would be uncountably many of these? Or do i need to write each u(n) as a decimal expansion using the numbers 0,1,2? To put it plainly, i'm very confused about what the question is asking so a point in the right direction would be much appreciated!

So while i realise i haven't had a proper attempt at a solution, with a nudge in the right direction hopefully i can get on my way and ask for some assistance if/when i need it showing all relevant work i've done.

Thanks everybody!