In LTI systems there are two famous functions the unit step function and the unit impulse functions. And they are defined as follows. $$ u[n] = \begin{cases} 1, & \text{if $n$ $\ge$ 0} \\ 0, & \text{if $n$ $\lt$ 0} \end{cases} $$ $$ \delta[n] = \begin{cases} 1, & \text{if $n$ $=$ 0} \\ 0, & \text{if n $\neq$ 0}. \end{cases} $$
They also define $u[n]$ as $$\sum_{k=-\infty}^{n} \delta[k]$$
Isn't this something like $ ... + \delta[-3] + \delta[-2] + \delta[-1] + \delta[0] + \delta[1] + \delta[2] + \delta[3] + ... + \delta[n]$ that gives just one(1)? Because $\delta[n] = 1$ when $n = 0$. How can we say it is a step function?