  Weyl defined real functions as mappings correlating each interval in  the choice sequence determining the argument with an interval in the  choice sequence determining the value “interval by  interval” as it were, the idea being that approximations to the input of the function should lead effectively to corresponding  approximations to the input. Such functions are continuous by  definition. Brouwer, in contrast, considers real functions as  correlating choice sequences with choice sequences, and the  continuity of these is by no means obvious. The fact that Weyl  refused to grant (free) choice sequences—whose identity is in  no way predetermined—sufficient individuality to admit them as  arguments of functions betokens a commitment to the conception of the continuum as a “medium of free Becoming” even deeper,  perhaps, than that of Brouwer.