I am reading definition of "path in topological space X", which is as follows:
" A path from a point $x$ to a point $y$ in a topological $X$ is a continuous function $f$ from the unit interval $[0,1]$ to $X$ with $f(0) = x$ and $f(1) = y$ "
My question is, why is path so defined? Why the choosen interval is $[0,1]$? Can't we take $[2,3]$? Why is the function taken to be continuous? Is the reason behind this, is that "path must be connected"? I am beiginner in topology! and to be obvious, anyone who does want to clear his concepts in topology, must know it! and, I don't want to "memories the definition without understanding it" as some people do!! Please help me...:-)