The Classical Fields: Structural Features of the Real and

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We see then that the derivative of the function at these fixed points greatly affects this convergence behavior. Think about a taxi driving you home from school. Some will say this is a book for mature math students, so any gaps should be filled in by the reader en route with pen and paper. Suppose that the universe contains only conventional matter sources (regular matter, dark matter and radiation, say), and suppose you know (you might question whether this is truly possible) that this is all it will ever contain.

Pages: 418

Publisher: Cambridge University Press; 1 edition (September 24, 2007)

ISBN: 0521865166

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The set A was clearly a failed attempt at building something with a c of ½. [As I recall, finding out it could only be an unsigned infinity was disappointing...] With hindsight, it's clear that there's a more compelling approach, based on another well-known property of c concerning cartesian products, which is worth preserving in any interesting extension of c: Using the 3 "axioms" of the previous article [and the value (-1)n which they impose for the c of ordinary n-dimensional Euclidean space] this relation can be easily established by [structural] induction for all "polyhedral" sets. (Such sets, which are the usual domain of definition of c, consist of finite unions of disjoint components, each homeomorphic to some n-dimensional Euclidean space, which are called its vertices, edges, faces, cells...) Therefore, the above relation does not contradict our three axioms and may be use as a fourth axiom in a larger scope of more general sets, which remains to be defined.. Topology and Geometry (Graduate Texts in Mathematics).

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