Surd synonyms

Since the fraction is infinite it cannot be commensurable and therefore its value is a quadratic surd number.

Consideration of the binomial theorem for fractional index, or of the continued fraction representing a surd, or of theorems such as Wallis's theorem (� 64), shows that a sequence, every term of which is rational, may have as its limit an irrational number, i.e.

Conversely every positive quadratic surd number, when expressed as a simple continued fraction, will give rise to a recurring fraction.

The second case illustrates a feature of the recurring continued fraction which represents a complete quadratic surd.