I am trying to teach myself computability theory with a textbook.
According to my book, a function $f$ over an alphabet $A=\{a, b, c, d, e, f, g, h, i, j, k, l, m, n, o, p, q, r, s, t, u, v, w, x, y, z\}$ is only computable iff the language
$$ L = \{s\#^j\sigma : s\in A^*, \sigma \in A, \text{ the }j\text{'th symbol of } f(s)\text{ is } \sigma\}$$
is decidable. Why is that? I don't understand because computability and decidability are 2 different concepts, right?