• to slowly approach a given destination; e.g. x-> 1/x converges towards 0 as x approaches infinity
  • to slowly approach the same point; e.g. in biology, two different species or some of their organs may experience convergent evolution
A sequence x (i.e. a function x mapping N to a metric space S) is said to converge if there exists an element L of S and a gauge function N:(0,infinity)->N such that for every positive real number e, d(x(n),L) < e whenever n > N(e). If this is the case, L is called the limit of the sequence x.

Theorem
A real sequence x:N->R converges if and only if there exists a guage function N:(0,infinity)->N such that for every positive real number e, d(x(n),x(m)) < e whenever n > N(e) and m > N(e).
This property is called the Cauchy criterion, and a sequence satisfying it is said to be a Cauchy sequence. The strength of this theorem is that it determines a necessary and sufficient criterion for convergence. However, it does not provide a method for determining the limit of a sequence; this is a much more difficult problem, and cannot be solved for a general sequence.


A function f:D->R is sait to converge at a point t in D provided that for some real number L and some guage function d:(0,infinity)->(0,infinity), one has:
For all e > 0, for all s in D, 0 < |s-t| < d(e) implies |f(s) - L| < e.
Then, L is said to be the limit of f at t.

Converge is perhaps one of the best know hardcore bands. Forming in the early nineties in Massachusetts, Converge started as many bands do just covering their favorite songs. They burst onto the hardcore scene shortly after forming with their first demo in early 1991. After this original demo the band held back for a short time compiling 2 other demos that better pulled their talents to change the current metal and hardcore scene which they themselves were not content with. These demos became the bulk of their full length debut “Halo in a Haystack.”

In mid-1995 Converge went even further with their progressive sound with the release of the EP “Unloved and Weeded Out.” This EP also noted the first real emergence of their classic songwriting abilities. Around this time Converge was touring the east coast and Canada making fans out of just about everyone that showed up for their shows with their unique metal/hardcore/punk mix.

Jumping forward another year Converge would release one of their most acclaimed CDs, “Petitioning the Empty Sky” on Ferret Records. This album featured their jackhammer like drumming, metal riffing, and what can best be described as scary singing. This album would later be re-released by Equal Vision because of it’s over all impressiveness.

Their next major release was many years in the making and was highly anticipated by many of their fans. However, “When Forever Comes Crashing” left many long time fans disappointed due to its slight departure from all the things that had made Converge great. This album featured fairly heavy vocal effects as well as a lack of breakdowns which left many people disappointed.

After this Converge released a number of various compellations and other samplers until there next big album came in mid-2001 with the release of “Jane Doe.” This album went back to their roots loosing the heavy vocal effects but keeping a good quality of production. This album is perhaps one of their most well known currently as it is very had to go to a hardcore show and not see at least half-a-dozen people wearing a Jane Doe shirt. Once again scary screaming and metal guitar were back in more than full force.

Currently Converge is still touring and working on releasing a new album and DVD. Converge’s live shows remain just as violent and intense as they were in the beginning, if not more so. As with many hardcore and metal bands this remains the best medium for enjoyment.

Converge is:

Con*verge" (?), v. i. [imp. & p.p. Converged (?); p.pr. & vb.n. Converging (?).] [Pref. con- + L. vergere to turn, incline; cf. F. converger. See Verge, v. i.]

To tend to one point; to incline and approach nearer together; as, lines converge.

The mountains converge into a single ridge. Jefferson.

 

© Webster 1913.


Con*verge", v. t.

To cause to tend to one point; to cause to incline and approach nearer together.

I converge its rays to a focus of dazzling brilliancy. Tyndall.

 

© Webster 1913.

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