Wikipedia defines a quasistatic process as "a thermodynamic process that happens infinitely slowly. However, it is very important of note that no real process is quasistatic. Therefore in practice, such processes can only be approximated by performing them infinitesimally slowly." I do not properly understand the definition. My problem lies with the mathematics of infinity and infinitesimal in the definition. Let's start with the prhase "a process that happens infinitely slow". Any process that starts to happen actually makes an increment (towards its final state) per unit of time. So, it will eventually reach its final state. But we would never want that to happen in reality because the process is meant to be completed in an infinite amount of time. So, the only logical conclusion is that the process 'does not happen at all'. Am I right? Assuming that I am right, let's now turn to the sentence "in practice, such processes can only be approximated by performing them infinitesimally slowly". Now, an infinitesimal increment IS an increment towards the final state. That means eventually the system will reach its final state. So, in practice we can allow the process can happen infinitesimally for us to reach the final state. Now here's the problem. Take a piece of unit length of some material and keep cutting it in half. Repeat the process for an infinite number of times and you should get an infinitesimal length. (Yes?) That implies that adding together infinitesimal amounts of lengths for an infinite number of times should give you the original finite length. (Or is it?) If that is so, how does that fit in with the riginal discussion regarding a quasistatic process?