Editing Existence theorem (section)

==Constructivist ideas==
From the other direction, there has been considerable clarification of what [[constructive mathematics]] is—without the emergence of a 'master theory'. For example, according to [[Errett Bishop]]'s definitions, the continuity of a function such as {{math|sin(''x'')}} should be proved as a constructive bound on the [[modulus of continuity]], meaning that the existential content of the assertion of continuity is a promise that can always be kept. Accordingly, Bishop rejects the standard idea of pointwise continuity, and proposed that continuity should be defined in terms of "local uniform continuity".<ref>{{Cite web|url=https://ncatlab.org/nlab/show/Bishop's+constructive+mathematics|title=Bishop's constructive mathematics in nLab|website=ncatlab.org|access-date=2019-11-29}}</ref> One could get another explanation of existence theorem from [[type theory]], in which a proof of an existential statement can come only from a ''term'' (which one can see as the computational content).