Heat capacity during state change

I read that the heat capacity of water when it is at 100 °C or 0 °C is infinite because all the heat given to it will not be used to increase temperature but to change the state.


I am unable to understand this. Say, we have water at 100 °C. If we continuously provide heat, water will change to steam and then it's temperature will increase, right?  

Sure, we'll have to provide more heat than before to break the bonds. But it will definitely become a 101 °C steam after a while.


So why is heat capacity infinite at state change?


