Indeterminate

The term "indeterminate" is sometimes used as a synonym for unknown or variable (Becker and Weispfenning 1993, p. 188).

A mathematical expression can also be said to be indeterminate if it is not definitively or precisely determined. Certain forms of limits are said to be indeterminate when merely knowing the limiting behavior of individual parts of the expression is not sufficient to actually determine the overall limit. For example, a limit of the form 0/0, i.e.,  where , is indeterminate since the value of the overall limit actually depends on the limiting behavior of the combination of the two functions (e.g., , while ).

There are seven indeterminate forms involving 0, 1, and :

(Thomas and Finney 1996, pp. 220 and 423; Gellert et al. 1989, p. 400). Note, however, that there is a certain ambiguity in this enumeration in the sense that symbolic expressions of the form  can perhaps be written as , etc.

If complex infinity  is allowed as well, then six additional indeterminate forms result:

The Wolfram Language returns the symbol Indeterminate upon encountering such expressions in the course of an evaluation.

The Wolfram Functions Site uses the notation > to represent an indeterminate quantity.

REFERENCES:

Becker, T. and Weispfenning, V. Gröbner Bases: A Computational Approach to Commutative Algebra. New York: Springer-Verlag, 1993.

Gellert, W.; Gottwald, S.; Hellwich, M.; Kästner, H.; and Künstner, H. (Eds.). Appendix, Plate 19. VNR Concise Encyclopedia of Mathematics, 2nd ed. New York: Van Nostrand Reinhold, 1989.

Thomas, G. B., Jr. and Finney, R. L. Calculus and Analytic Geometry, 8th ed. Reading, MA: Addison-Wesley, 1996.