[FOM] the real intermediate value theorem

[Peter Schuster]

Every line drawn by a pencil necessarily has a certain width, no matter how 
sharp the pencil is. Therefore rather the approximate intermediate value 
theorem is suited for real-world functions, than its customary exact variant. 
The former has a constructive proof anyway, whereas the latter has one 
provided that the function satisfies some mild preconditions. These extra  
requirements, moreover, are met by all the real-analytic functions, which 
doubtlessly include most of the continuous functions that are of relevance 
in science. Needless to say, each of the proofs contains an algorithm in a 
fairly explicit way. See the index entries for "intermediate value theorem" 
in books like the ones by Bishop, Bishop/Bridges, and Troelstra/van Dalen. 

Peter Schuster

Mathematisches Institut
Universitaet Muenchen