Infinitesimals. Hyperreal Numbers

... to be continued ...

References

1. P. J. Davis & R. Hersh, The Mathematical Experience, Houghton Mifflin Co, 1981, 237-254
2. K. Ito, Nonstandard Analysis (293), in Encyclopedic Dictionary of Mathematics, v. 1, MIT Press, Press, 2000 (fourth printing), pp. 1100-1103
3. A. Robinson, Non-standard Analysis, Princeton University Press (Rev Sub edition), 1996
4. I. Stuart, Nonstandard Analysis, in R. Courant and H. Robbins, What Is Mathematics?, Oxford University Press, 1996, pp. 518-524
5. I. Stewart, Non-Standard Analysis, in From Here to Infinity: A Guide to Today's Mathematics, Oxford University Press, 1996, pp. 80-81.

Philip Apps

http://en.wikipedia.org/wiki/Non-standard_analysis

• What Is Infinity?.
• Infinity As a Limit.
  • Infinite Sums and Products
• Cardinal Numbers.
  • Cantor-Bernstein-Schroeder theorem.
• Ordinal Numbers.
  • Order. Well-ordered sets.
• Surreal Numbers.
• Infinitesimals. Hyperreal Numbers
• Various Geometric Infinities
  • Projective Infinity.
  • Infinity in Inversive Geometry.
  • Infinity in Compactification.
• Paradoxes of Infinity
  • Achilles and the Tortoise
  • Infinity and Probability
  • Infinite Border, Finite Area