It depends on the range of your t variable and how finely you want to represent that.
If 0<=t<=1, then you can't represent it in a computer with an infinite number of values (continuously), but you can do:
t = 0:0.001:1;
represent it in increments of 0.001. Or
t = linspace(0,1,1000);
For example:
t = 0:0.001:1;
x = sin(t);
plot(t,x)
In a "vectorized" language like MATLAB, it is often better to represent things as vectors, or matrices when possible, and then evaluate things over that set, so your "for all t" becomes:
1.) define a vector of t values
2.) evaluate something over for all t in that set
