Definitions
from Wiktionary, Creative Commons Attribution/ShareAlike License
 adj. Not integer
 n. Any number that is not an integer, but especially a real number
Etymologies
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Examples

Strange attractors also are often characterized as possess noninteger or fractal dimension (though not all strange attractors have such dimensionality).

Roughly this means that if we try to apply the same procedure of “filling” the structure formed by the strange attractor with small squares or cubes, in the limit as Îµ approaches zero the result is noninteger.

Whether one is examining a set of nonlinear mathematical equations or analyzing the time series data from an experiment, the presence of selfsimilarity or noninteger dimension are indications that the chaotic behavior of the system under study is dissipative (nonconservative) rather than Hamiltonian

Further review suggests that the complex variable expansion may not be valid for a fraction noninteger, but will check another book at work.
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