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The Bolzano-Weierstrass theorem asserts that every bounded sequence of real numbers has a convergent subsequence. More generally, it states that if is a closed bounded subset of then every sequence in has a subsequence that converges to a point in. This article is not so much about the statement, or its proof, but about how to use it in applications.Combinatorial Nullstellensatz Noga Alon Abstract We present a general algebraic technique and discuss some of its numerous applications in Combinatorial Number Theory, in Graph Theory and in Combinatorics. These applications in-clude results in additive number theory and in the study of graph coloring problems. Many of these are known results, to which we present uni ed proofs, and some.Issuu is a digital publishing platform that makes it simple to publish magazines, catalogs, newspapers, books, and more online. Easily share your publications and get them in front of Issuu’s.
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