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A positive real number r is represented by a, potentially infinite,
continued fraction
:
The restriction on the last term, , 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:
Operations are also handled as per decimal expansions.
See [15, 46] for further details concerning this representation
and associated methods.
Next: 2.15.5 Converging Intervals
Up: 2.15 Real Representations
Previous: 2.15.3 Decimal Expansions