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Never changing.

*‘the pattern of cell divisions was found to be invariant’**‘Skuladottir and Charnov collaborated on a paper in 2000 predicting that indeed there are invariant rules for sex change and presenting shrimp data to bolster their claim.’**‘The open time constants are invariant to ligand concentrations, suggesting that ligand binds exclusively to the closed channel.’**‘The results reveal 23 nonsynonymous changes and 127 invariant sites in total in the hinge region.’**‘This term is invariant to the change in reference genotype that allowed us to derive this equation.’**‘So looking at whether something makes people happy is largely futile. In statisticians' terms, you are looking for variance in something that is invariant.’**‘In villages, families throng at the lone hand pump for the stuff: this is a sight that is so invariant in India that you might be forgiven for thinking hand pumps go back to Vedic times.’**‘Further analysis of the data revealed the presence of at least two fluorescent species and fitting to a bi-exponential model was performed assuming invariant lifetimes.’**‘One of the diverged phenotypes in cultivated rice is observed in the patterns of coloration due to anthocyanin pigmentation in spite of invariant pigmentation in the wild forms of rice.’**‘Absence of major oceanographic anomalies in the immediate vicinity of Johnston Atoll may contribute to relatively high and invariant survival in Brown Boobies.’**‘However, the scholarship of revivals has not emphasised the possibility of significant invariant qualities in appropriated or ‘revived’ folk culture.’**‘As outlined above, we assumed that both environmentally induced variability and colony growth rates were relatively invariant within a population.’**‘Results for ecstasy and traditional hard drug users were highly invariant, but the ecstasy users' rate of previous hard drug use was much higher than that of any other group.’**‘In contrast, was relatively invariant among populations because the number of segregating sites was largely determined by the presence of both alleles.’**‘Replacement substitutions are extremely variable in rate, ranging from many sites that are essentially invariant to a few that evolve fairly rapidly.’**‘Consistent with the close phylogenetic relationships of the species sampled, most nucleotide sites were invariant in pair wise comparisons.’**‘Among women, the long-term health effects of early parental support also appeared to be relatively invariant, with one exception.’**‘All these are invariant in our sequences, of both sets A and B.’**‘The interactions of the individual dipoles in a magnet do not depend on any particular direction, and their dynamics are rotationally invariant.’**‘For a transactional leader, there are no universal invariant principles, policies, or goals applicable to all situations and at all times.’**‘As in all mixture problems, this model is not identifiable as the likelihood is invariant under any relabeling of the populations.’*

**unalterable**, immutable, invariable, unvarying, invariant, changeless, firm, fixed, hard and fast, cast-iron, set in stone, set, decided, established, permanent, deep-rooted, enduring, abiding, lasting, indestructible, ineradicable, irreversible, unfading, constant, perpetual, eternal, lifelong

### noun

MathematicsA function, quantity, or property which remains unchanged when a specified transformation is applied.

*‘For example, in Euclidean geometry, the relevant invariants are embodied in quantities that are not altered by geometric transformations such as rotations, dilations, and reflections.’**‘Under their direction he laid the basis for the important work he was later to achieve in the fields of foundations of geometry, projective geometry, topology, differential invariants and spinors.’**‘At Freiburg, he took a course with Oskar Bolza on the theory of invariants, and a course on differential geometry and a history seminar with Alfred Loewy, one of the two professors at Freiburg.’**‘Todd generalised the arithmetic genus and the invariants of the canonical system on an algebraic variety to a system of invariants of every codimension.’**‘Also in 1887 Voigt first wrote down the transformations and showed that certain equations were invariant under these transformations.’*

**Pronunciation**

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