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Home Real and Hyperreal Numbers Infinitesimal, Finite and Infinite Numbers Examples Example 7
 
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Example 7

If H is positive infinite then, surprisingly,

01_real_and_hyperreal_numbers-117.gif

is infinitesimal.

This is shown using an algebraic trick.

01_real_and_hyperreal_numbers-118.gif

The numbers H + 1, H - 1, and their square roots are positive infinite, and thus the sum 01_real_and_hyperreal_numbers-119.gif+ 01_real_and_hyperreal_numbers-120.gifis positive infinite. Therefore the quotient

01_real_and_hyperreal_numbers-121.gif

a finite number divided by an infinite number, is infinitesimal.
Home Real and Hyperreal Numbers Infinitesimal, Finite and Infinite Numbers Examples Example 7

Last Update: 2006-11-15