Algebraic Systems
... 2 cannot be expressed as a quotient of two integers. The climax of the ancient theory ( and practice) of numbers was the invention of zero. Zero was invented several times, independently, in different parts of the world, and eventually was imported to Europe from India, by Arab merchants in the Midd ...
... 2 cannot be expressed as a quotient of two integers. The climax of the ancient theory ( and practice) of numbers was the invention of zero. Zero was invented several times, independently, in different parts of the world, and eventually was imported to Europe from India, by Arab merchants in the Midd ...
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... • k · k defines a metric d on A given by d(a, b) = ka − bk, so that A with d is a metric space and one can set up a topology on A by defining its subbasis a collection of B(a, r) := {x ∈ A | d(a, x) < r} called open balls for any a ∈ A and r > 0. With this definition, it is easy to see that k · k is ...
... • k · k defines a metric d on A given by d(a, b) = ka − bk, so that A with d is a metric space and one can set up a topology on A by defining its subbasis a collection of B(a, r) := {x ∈ A | d(a, x) < r} called open balls for any a ∈ A and r > 0. With this definition, it is easy to see that k · k is ...
