| 释义 |
hyperreals An extended version of the real numbers that includes infinite and infinitesimal elements. A hyperreal is an equivalence class of a real sequence, with a real number x identified with the constant sequence {x}, while the sequence {n} is an infinite hyperreal with its reciprocal {1/n} being an infinitesimal. When algebraic operations are defined componentwise, the ring of sequences has zero-divisors; to avoid this, two sequences are made equivalent if they agree for almost all components (in a technical sense) so that {a}{b}={0} if and only if {a}={0} or {b}={0}. The hyperreals then form a field. The study of the hyperreals is called non-standard analysis, though this term is sometimes more broadly used.
|