MATH 1251 Lecture Notes - Infinitesimal

• School: Northeastern University
• Department: Mathematics
• Course: MATH 1251
• Professor: Sandy Blank

Document Summary

Infinite numbers- bigger than any standard number (h-1, h, h+1, h+2) * h divided by any standard # = infinite # * h2, h3, h, 3 h are still infinite. * standard mathematical rules apply h0 = 1, not infinite; h/a = a 0; 1h. Moderate numbers- standard number +/- infinitesimal number (1+e, 3e+2, Infinitesimal numbers- smaller than any standard number (-e, e, e2) * 0 is the only standard infinitesimal number. * e2 < e because any # < 1, squared, = a smaller number. * 1/h= an infinitely small positive number < 1. Examples: e2 2e + 1 + 1/h = moderate number. Infinitesimal number infinitesimal number = infinitesimal number. Moderate number + infinitesimal number = moderate number. H 2 1: h 2 1. 3h2+ h-2 3h2+ h-2 /h2 3+ 1/h 2/h2 moderate. E 2 e: e 2 e.