Jacques Carette answer to Lennart Augustsson's comment of:
Such people have the nasty habit of also thinking that ALL functions are continuous! You might think they were constructivists or something.
Why would a constructivist think that all functions are continuous?
That would be a theorem of construtive mathematics! All *constructible* functions are continuous. See http://plato.stanford.edu/entries/mathematics-constructive/
J. referenced this in his answer to my own doubts, where I confessed that I knew physicists who sympathise with constructivists, yet they 'somehow' accept that quantum scattering amplitudes must have branch cuts... According to Jacques this cannot hold, since a True Constructivist rejects the equality of reals. == Well, I read once in Drexler Mathematical Forum (was it Barr?) that Bishop himself didn't consider the claim that all functions are continuous as theorem. This is not provable. A kind of auto-trap? I am lost. In Recursive Constructive Math there is a theorem of Kreisel-Lacombe- Shoenfield-Tsejtin that total function within separable metric spaces are continuous, but the assumptions are quite strong... All this is very far from my everyday soup, and I respect True Mathematicians who split the hair infinitely very much (and also constructivists and intuitionists who refuse this splitting as a non-constructive, infinite process...) But, since the notion of function and of reals differs somehow from the classical counterparts, as far as a poor physicist speaks about entities which belong to the REAL WORLD, the problem remains, since even Master Yoda doesn't know which should be the structure of math relevant to the reality. I mean the 'true' math. And of course, with True meaning of the word 'true', provided we know what does it mean the word 'meaning'. Thank you truly. Jerzy K. (Kafka created at least two heroes named K., in The Trial, and in The Castle. I feel like both of them together...)