# Defining bound on input signal to test accumulator for BIBO stability

For an accumulator, defined as shown in the image below, why would I define $$B_x=1$$? $$u[n]$$ is defined at zero so my (possibly misguided intuition) is telling me that I'd choose $$B_x = 0$$ to not eliminate that point.

$$B_x$$ is a bound on the magnitude of the input signal. So if $$x[n]=u[n]$$ you have $$|x[n]|\le1$$ and, consequently, $$B_x=1$$ is a valid bound on $$|x[n]|$$. $$B_x=0$$ would mean that the input signal is zero.