We have now obtained three different but equivalent forms of the fundamental axiom (the fundamental axiom itself, the existence of a supremum for a non-empty bounded set, and the Bolzano-Weierstrass theorem) and used methods based on these three forms to prove the intermediate value theorem and the mean value inequality (themselves equivalent to the fundamental axiom). I make no excuse for the time we have spent on this programme. All of analysis rests like an inverted pyramid on the fundamental axiom so it makes sense to study it closely.