Kategoria BISAC: Mathematics >> Set Theory

Handbook of Mathematical Induction: Theory and Applications shows how to find and write proofs via mathematical induction. This comprehensive book covers the theory, the structure of the written proof, all standard exercises, and hundreds of application examples from nearly every area of mathematics.

In the first part of the book, the author discusses different inductive techniques, including well-ordered sets, basic mathematical induction, strong induction, double induction, infinite descent, downward induction, and several variants. He then introduces...

The first critical work to attempt the mammoth undertaking of reading Badiou's Being and Event as part of a sequence has often surprising, occasionally controversial results.

Looking back on its publication Badiou declared: "I had inscribed my name in the history of philosophy." Later he was brave enough to admit that this inscription needed correction. The central elements of Badiou's philosophy only make sense when Being and Event is read through the corrective prism of its sequel, Logics of Worlds, published nearly twenty years later.

At the same time...

The first critical work to attempt the mammoth undertaking of reading Badiou's Being and Event as part of a sequence has often surprising, occasionally controversial results.

Looking back on its publication Badiou declared: "I had inscribed my name in the history of philosophy." Later he was brave enough to admit that this inscription needed correction. The central elements of Badiou's philosophy only make sense when Being and Event is read through the corrective prism of its sequel, Logics of Worlds, published nearly twenty years later.

At the same time...

The book introduces a new model of orders of magnitude and of error analysis, with particular emphasis on behaviour under algebraic operations. The model is formulated in terms of scalar neutrices and external numbers, in the form of an extension of the nonstandard set of real numbers. The book starts with detailed presentation of the algebraic structure of external numbers, then deals with the generalized Dedekind completeness property, applications in analysis, domains of validity of approximations of solutions of differential equations, particularly singular perturbations. Finally, it...