Exponents

The following rules apply for exponents that are positive integers. The justification is sketched here.   These rules are also said to apply for exponents that are not positive integers–that is, zero and…

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Irrational Numbers

Are rational numbers the only numbers? The continuity of real numbers is an assumption in the Cantor-Dedekind axiom [1]. The idea of continuity brings up the possibility of a different type of number…

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Definition of a Sequence

The title of Section 2 in book [1] is Sequences of rational numbers. At the beginning of this section, a definition is provided for a sequence, and I quote it here. Definition. If,…

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Fundamental Laws of Arithmetic

Here is a continuation of this post. Long story short, I am learning number theory from a book [1]. The author of this book [1] begins his own analysis of number theory with the “system…

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