indeterminate

English

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Pronunciation

• IPA(key): /ɪndɪˈtɜː(ɹ)mɪnət/

indeterminate (comparative more indeterminate, superlative most indeterminate)

1. Not accurately determined or determinable.
2. Imprecise or vague.
3. (mathematical analysis, of certain forms of limit) Not definitively or precisely determined, because of the presence of infinity or zero symbols used in any of several improper combinations.
4. (biology, of growth) With no genetically defined end, and thus theoretically limitless.
5. () Not topped with some form of terminal bud.
6. Intersex.
7. Designed to allow the incorporation of future changes whose nature is not yet known.
• 2014, David Oakley, The Phenomenon of Architecture in Cultures in Change, page 196:
It bears an affinity to the problem of indeterminate architecture—the indeterminate residential area.

Noun

indeterminate (plural indeterminates)

1. (algebra, strict sense) A symbol that resembles a variable or parameter but is used purely formally and neither signifies nor is ever assigned a particular value;
(loose sense) a variable.
• 1862, H. J. Stephen Smith, Report on the Theory of Numbers—Part III, Report of the 31st Meeting of the British Association for the Advancement of Science, British Association for the Advancement of Science, page 292,
The form is linear, quadratic, cubic, biquadratic or quartic, quintic, &c., according to its order in respect of the indeterminates it contains; and binary, ternary, quaternary, &c., according to the number of its indeterminates. Thus ${\displaystyle x^{2}+y^{2}}$  is a binary quadratic form, ${\displaystyle x^{3}+y^{3}+z^{3}-3xyz}$  is a ternary cubic form.
• 1892, Henry B. Fine, Kronecker and His Arithmetical Theory of the Algebraic Equation, Thomas S. Fiske, Harold Jacoby (editors), Bulletin of the New York Mathematical Society, Volume 1, New York Mathematical Society, page 179,
Such a factor is therefore an integral function of ${\displaystyle x}$  and the indeterminates ${\displaystyle u_{1},u_{2},\dots u_{n}}$  with coefficients belonging to the domain of rationality ${\displaystyle (R',R'',..)}$  and may be represented by ${\displaystyle g(x,u_{1},u_{2},..u_{n})}$ .
• 2006, Alexander B. Levin, Difference Algebra, M. Hazewinkel, Handbook of Algebra, page 251,
Let ${\displaystyle T=T_{\sigma }}$  and let ${\displaystyle S}$  be the polynomial ${\displaystyle R}$ -algebra in the set of indeterminates ${\displaystyle \left\{y_{i,\tau }\right\}_{i\in I,\tau \in T}}$  with indices from the set ${\displaystyle I\times T}$ .

Usage notes

The distinction between indeterminate and variable when discussing, say, a polynomial, is often overlooked: an indeterminate is regarded as a type of variable. In fact, the distinction relates to the context: i.e., whether one is discussing a polynomial per se (a formal expression consisting of coefficients and indeterminates) or the function that the polynomial represents when the indeterminate is considered a variable. Moreover, some authors choose to use the terms indeterminate and variable interchangeably.