I have read in an article that 'We do not define $u(t)$ at $t=0$. At $t=0$ we think of it as in transition between $0$ and $1$'.
The domain of the Unit step function is the real numbers, but if $u(t)$ isn't defined at $t=0$ then it isn't function, right?
But then, why do we call this Unit step function a "function"? Or is the above quote from the article wrong?