Ok everyone, so I was reading about computability when I came across the following-
''Suppose that $f(x, z)$ is any function; the bounded sum $\sum_{z<y} f(x, z)$ is a function of $x, y$ given by the following recursion equation:
$\sum_{z<0} f(x, z) = 0$
$\sum_{z<y+1} f(x, z) = \sum_{z<y} f(x, z)$ + $f(x, y)$"
I have never seen sigma notation using the less-than symbol like this before, and I've been thinking about it for hours and have no idea of how to interpret it. It would be super helpful if someone could give an example as well, say if the function $f(x, z)$ in the above passage were the addition function or something (i.e. $f(x, z) = x + z$).