Why they chose maximum and not minimum functions

[transgalactic]

in every example in this article
it uses minimum function because we need to squeeze the function
as close as possible to the limit(example 4).
http://www.mathhelpforum.com/math-h...e-never-learnt-well-epsilon-delta-proofs.html
but i got this proove that use maximum.
http://img440.imageshack.us/img440/9160/25023372lz4.gif

why?

 

[HallsofIvy]

It's not clear what your question is. In the first example you give, they have $|x-a||x-b|< \epsilon$ in order to get |x-a| only, you have to divide both sides by |x-b| "inverting it reverses the inequality. That doesn't happen in the second example- there is no reciprocal.

 

[transgalactic]

when to use MAX when to use MIN ?