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Home Real and Hyperreal Numbers Infinitesimal, Finite and Infinite Numbers Examples Example 2
 
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Example 2

The quotient

01_real_and_hyperreal_numbers-108.gif

is infinitesimal, provided ε ≠ 0. The given number is equal to

(1)

01_real_and_hyperreal_numbers-109.gif

We see in turn that ε, ε2, ε3, ⅓ε, -8/3 ε2, 5/3 ε3 are infinitesimal; hence the sum (1) is infinitesimal.
Home Real and Hyperreal Numbers Infinitesimal, Finite and Infinite Numbers Examples Example 2

Last Update: 2006-11-15