The definitions of 1 to 3 are correct. Only the 4th is wrong as already said in post #8.
Definition: A discrete-time signal is mathematically represented by a
sequence of values e.g. {x[k]} where "k" goes from -infinity to + infinity
The discrete signal is written like this: {x[k]}={0,0,0,...,1,1,1,1,1,0,0,0,0....}
The digital signal is written like this: f(x)=0 when -infinity<x<alpha and x>whatever, and 1 when alpha<x<whatever
- - - Updated - - -
The key point to understand the difference between discrete-time signal and digital or whatever is the following:
"k" can only be an
integer value (negative as well) i.e. in maths the integer values are in the
Z set.
For example, if someone asks you for the sequence value of x[3.5312] it does
not exist whereas if someone asks you for the value at f(3.5312) of a digital signal it could be e.g. high or low but it
does exist.
A sequence can not be mathematically defined for non integer values of its independant variable "k".