(analysis) A sequence in a metric space with metric d is convergent to a point , denoted as , if for every there is a natural number N such that for every : .
(mathematics) The rational number obtained when a continued fraction has been terminated after a finite number of terms.
Other Word Forms
Convergent Sentence Examples
Note that the funnel in Figure 4 is also a convergent nozzle.
The general continued fraction al is evidently equal, convergent by convergent, to the continued fraction X 2 b 2 X2X3b3 x3%4b4 a1+ A2a2 + X + X
Every even convergent is greater than every odd convergent; every odd convergent is less than, and every even convergent greater than, any following convergent.
Every convergent is a nearer approximation to the value of the whole fraction than any fraction whose denominator is less than that of the convergent.
The difference between the continued fraction and the nth convergent is less than, and greater than a n+2 These limits qn may be replaced by the following, which, though not so close, are simpler, viz.