How to prove that a straight line is an infinite set of points? From the basic elementary level when we start reading geometry we get this idea developed in us that a straight line is the conjuction of infinite points.but how to prove this?  I mean is this an axiom or its provable? 

Take your endpoints, call them $S$ and $E$. Pick some point between $S$ and $E$, let us call it $M$. Then, pick a point between $S$ and $M$. Call it $M_2$. Pick a point between $S$ and $M_2$ .... 
If you can keep going like that, it is easy to see that the line must have infinite points... and you can keep going on like that. The numbers don't just end. 
