<P> In Stephen Kleene's discussion of cardinal numbers in Kleene 1952, he uses "mutually exclusive" together with "exhaustive": </P> <Dl> <Dd> "Hence, for any two cardinals M and N, the three relationships M <N, M = N and M> N are' mutually exclusive', i.e. not more than one of them can hold . ¶ It does not appear till an advanced stage of the theory...whether they are' exhaustive', i.e. whether at least one of the three must hold". (italics added for emphasis, Kleene 1952: 11; original has double bars over the symbols M and N). </Dd> </Dl> <Dd> "Hence, for any two cardinals M and N, the three relationships M <N, M = N and M> N are' mutually exclusive', i.e. not more than one of them can hold . ¶ It does not appear till an advanced stage of the theory...whether they are' exhaustive', i.e. whether at least one of the three must hold". (italics added for emphasis, Kleene 1952: 11; original has double bars over the symbols M and N). </Dd>

What is the difference between mutually exclusive and collectively exhaustive events