Approximation

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approximation

[ə¦präk·sə¦mā·shən]
(mathematics)
A result that is not exact but is near enough to the correct result for some specified purpose.
A procedure for obtaining such a result.

Approximation

 

replacement of certain mathematical objects by others which are in one sense or another close to the initial objects. Approximation makes it possible to study the numerical characteristics and qualitative properties of the object, reducing the problem to a study of simpler or more convenient objects—for example, objects whose characteristics are easily computed or whose properties are already known. The theory of numbers studies Diophantine approximations—in particular, approximations of irrational numbers by rational numbers. Approximations of curves, surfaces, spaces, and mappings are investigated in geometry and topology. Some branches of mathematics are wholly devoted to approximations, as, for example, the approximation and interpolation of functions and numerical methods of analysis. The role of approximation in mathematics is continually growing. Presently, approximation can be viewed as one of the basic concepts of mathematics.

S. B. STECHKIN

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2) shares approximately equal to the number of shares expected to be issued under First Union's Dividend Reinvestment and Stock Purchase Plan and employee stock purchase and stock compensation plans; and
As in the UCLA study, the new and old vaccines boosted pertussis antibodies in approximately equal measures, and side effects with the new vaccine were significantly rarer than with the old one.
The Fund offered to repurchase up to 5% of its outstanding shares of common stock for cash at a price approximately equal to net asset value as of October 20, 2006.