This is a response to the following question posted by fiftyducklings as a comment to Fraction Satisfaction:
In geometry, we learned things like “segment addition postulate” and “area addition postulate,” which were pretty intuitive statements. But then I looked at Euclid’s five postulates, and although he included several intuitive statements, he never bothered to list the “postulates” listed above. Would those statements be considered too intuitive to bother to list? Or is there actually a way to prove them (not demonstrate them)? Because I used to think they were too obvious to bother to attempt to prove, and then I found about the whole Banach-Tarski sphere dissection…
Your questions seem to be about what should or should not be explicitly stated as a postulate and whether or not it is necessary to provide proofs for “obvious” statements. Your questions raise a number of complex issues and their answers depend on context. Here are some comments. Continue reading
s to be a willing, albeit wacky, interviewee: 
for their annual Pi Day contest). Because of this extra inducement, I gave our members an extra challenging problem: 
