Is it permissible to fast the entire month of Allah, Al-Muharram?

Fasting frequently in the month of Muharram is a prescribed act, and whoever fasts the entire month has done well. The proof for this is the Prophet's (peace and blessings be upon him) saying: "The best fasting after Ramadan (definition) is Allah's month which you call Muharram." It is possible that this might mean fasting the entire month of Muharram, or that the intention is to fast the Day of Ashura because it falls within it. However, the apparent meaning is the entire month of Muharram. The more a servant fasts therein, the greater his reward will be.