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Title: seems ok at first glance...
Review: ..but has inadmissable lapses in rigor. The first shock came when this book "proved" that every infinite set has a countable subset, without even mentioning that the axiom of choice is necessary for this. In another place, a theorem proof took a set satisfying certain assumptions, removed elements from it according to some procedure, and went on assuming that the reduced set still satisfied the assumptions. This is the general attitude of this text. It's clear and fresh, but the proofs just aren't up to standard. We are dealing with a subject here whose sole purpose is precise aximatization, and painstaikingly rigorous proofs...but this book seems to ignore this attention to detail.Get the text only as a light reading supplement....but don't read it for it's rigor, because there isn't any.
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