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Usefulness of multiple undo 

This is a response to Sean�s inquiry in the thread �FM 7: A sad update� as to the usefulness of multiple undo. In that thread, my message is 41, while Sean�s reply is 42. In order to keep the threads more focused, I wish to address the topic of multiple undo in this thread. 

It can be shown that, given the usefulness of single undo, the usefulness of multiple undo is a logical necessity. I have identified two proofs of this statement: an inductive proof and an amalgamative proof. Keep in mind that, in mathematical terms, the concept that undo is useful means that the probability that undo is useful is non-zero. 

Inductive proof: 

Given the usefulness of single undo, once single undo has been performed, the usefulness of single undo now applies if the sequence of executed commands hasn�t been exhausted. This implies that a second level of undo is useful, ad infinitum. Therefore, given the usefulness of single undo, the usefulness of multiple undo follows. 

Amalgamative proof: 

The user may define a single action as consisting of an arbitrary sequence of program commands, in which case the program will need multiple undo in order to implement what for the user is single undo. Therefore, given the usefulness of single undo, the usefulness of multiple undo follows. 

Note that in the general case the sequence of commands to be undone is not necessarily a subsequence consisting of the most recently executed commands. The general case was suggested by Sheila Carlisle in message 18. However, I�ve never heard of a program that implements the general undo concept. Has anyone else? 

In conclusion, since the usefulness of multiple undo is a logical necessity given the usefulness of single undo, any argument for the usefulness of single undo is an argument for the usefulness of multiple undo. Consequently, unless someone wishes to argue against the usefulness of single undo, we may assume that the usefulness of multiple undo is established.