Why is the money supply perfectly inelastic? From my notes:

We analyze the determination of the interest rate using a supply/demand model relating the interest rate (price of money) to the quantity of money. Since we assume:

1) no excess reserve

2) no excess currency in circulation

Real money supply (Ms/P) does not change with with a change in the interest rate, thus perfectly inelastic Ms

This is the part I don't really get. If money supply is determined by the central bank/government, does my notes have any connection to understanding why money supply is inelastic?
The Fed controls the nominal money supply as they are the only ones who can add or remove money from the economy by printing it. Real money supply is only affected by increases or decreases in inflation and is fixed assuming inflation is 0. In the IS-LM model which is what I assume you are referring to it is assumed that inflation is fixed or that the fed will maintain the real money supply at a given point by changing the nominal money supply for given price levels.

Graphically money supply can be shown like so:


The equilibrium between money supply (which is set by the fed) and money demand (which is set by economic factors) generates the interest rate for the economy at a given time. The fed thus has power to affect the interest rate by increase or decrease the real money supply in order to maintain an interest rate. Given that the fed has complete control over the interest rate under this model it is often assumed that LM is horizontal due to the fact that the fed can set whatever rate they choose regardless of economic factors.