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2.15.4 Continued Fractions

A positive real number r is represented by a, potentially infinite, continued fraction
tex2html_wrap_inline33731 :

displaymath8925

The restriction on the last term, tex2html_wrap_inline33733 , enforces a unique representation for each real number. The continued fraction is finite if and only if r corresponds to a rational number. Euclid's algorithm is used to determine the sequence of terms for a given real number. There is a unique representation for each real number, as with decimal expansions, so:

figure8938

Operations are also handled as per decimal expansions.

See [15, 46] for further details concerning this representation and associated methods.

next up previous notation contents
Next: 2.15.5 Converging Intervals Up: 2.15 Real Representations Previous: 2.15.3 Decimal Expansions
Jeff TupperMarch 1996