Real Analysis (Cantors Diagonalisation?)

[patata]

Homework Statement

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

Describe a set of countable functions from S

Homework Equations

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

The Attempt at a Solution

To begin with, I am 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 realize 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!

 

[LCKurtz]

OK, I'll take a guess at what you are supposed to do. Each of your functions maps N to {0,1,2} so is essentially a sequence of these numbers. For example, one such function u might have u(1)=2, u(2) = 1, u(3) = 1, u(4) = 0, ... which is essentially the sequence

u = 2,1,1,0,...

I'm guessing here, but I wonder if your exercise is to use a Cantor type argument to prove that the set of such functions is uncountable.