Hyperreal: Ultrafilter Construction of the Non-Standard Reals
See J. D. Fleuriot and L. C. Paulson. Mechanizing Nonstandard Real
Analysis. LMS J. Computation and Mathematics 3 (2000), 140-190.
- Filter
Theory of Filters and Ultrafilters.
Main result is a version of the Ultrafilter Theorem proved using
Zorn's Lemma.
- HLog Non-standard logarithms
- HSeries Non-standard theory of finite summation and infinite series
- HTranscendental Non-standard extensions of transcendental functions
- HyperDef
Ultrapower construction of the hyperreals
- HyperNat Ultrapower construction of the hypernaturals
- HyperPow Powers theory for the hyperreals
- IntFloor Floor and Ceiling functions relating the reals and integers
- Integration Gage integrals
- Lim Theory of limits, continuous functions, and derivatives
- Log Logarithms for the reals
- MacLaurin MacLaurin series
- NatStar Star-transforms for the hypernaturals, to form non-standard extensions of sets and functions involving the naturals or reals
- NthRoot Existence of n-th roots of real numbers
- NSA Theory defining sets of infinite numbers, infinitesimals, the infinitely close relation, and their various algebraic properties.
- Poly Univariate real polynomials
- SEQ Convergence of sequences and series using standard and nonstandard analysis
- Series Finite summation and infinite series for the reals
- Star Nonstandard extensions of real sets and real functions
- Transcendental Power series and transcendental functions
Last modified on $Date: 2004/04/19 11:49:35 $
lcp@cl.cam.ac.uk