Tag
Convergence
Entries tagged convergence.
3 entries
Concept
Infinite sequences and convergence
A sequence converges to a value when, no matter how small a tolerance you demand, all but finitely many of its terms fall within that tolerance of the value, and this precise test is what separates an endless procedure that settles from one that merely keeps changing forever.
7 min
ConceptLimits as controlled approach
A limit is a precise, checkable statement about what value a quantity gets forced arbitrarily close to as an input approaches a point, without ever requiring the input to actually reach that point.
7 min
ConceptSeries as accumulated sequences
A series is not a mysterious act of adding infinitely many numbers at once but an ordinary sequence of running totals, called partial sums, and the series has a sum precisely when that sequence of totals converges.
7 min