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to diverge

to diverge

1 9.6
In math, to grow without stopping at any number
  • verb
  • /dɪˈvɜrdʒ/
  • Specialized
translation icon : divergir
  • The velocity is found to diverge as ln(ln N) in the large population limit.

One possibility is that this curve just diverges as Z approaches one.

Examples

  • If this integral diverges, then your series diverges.

  • As the equation was simplified, the terms began to diverge, leading to an unbounded solution.

  • The first two methods diverge in their predictions when the velocity approaches its maximum value.

    Academic text (1997)
  • If the model diverges from reality, there's something wrong with the model, not with reality.

    Blog text (16)
  • One possibility is that this curve just diverges as Z approaches one.

  • Although the conductivity is finite at all finite temperatures, he says, it does appear to diverge as the temperature heads toward absolute zero.

    Academic text (2004)
  • Extrapolating back in time, the time series diverges from the recent linear trend about 16 years ago.

    Blog text (31)
  • Small variations in input—within the range of feasible inputs—cause the solution to diverge exponentially with time.

    Blog text (34)
  • The series of calculations will diverge if the initial values are not properly defined.

  • In this scenario, the results will diverge to infinity, indicating the model's limitations.

Antonyms

51 5.5

To come together from different places and meet at one point

to converge
  • Specialized
3 6.6

To get closer to a fixed number as more terms are added or as a variable changes

Surface Forms

diverge infinitive
diverged past
diverged past participle
diverging present participle
diverges third person singular

Morphology

diverge = verge (semi-transparent) = di + verge

Morphologically similar to sense 1 ('di-' + 'verge'), but the mathematical meaning is a specialized extension (technical) rather than an immediately obvious literal combination.

Etymology

Diverge comes from parts meaning 'apart' (di-) and 'to turn' (vergere). A helpful way to remember the math sense is to picture sums or numbers 'moving apart' and growing with 'no limit', which is why a series that keeps growing is said to diverge.