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What does incongruent mean?

Looking for the meaning or definition of the word incongruent? Here's what it means.

Adjective
  1. out of place, incompatible, inharmonious, not congruent
  2. (mathematics) of or relating to two numbers that have different remainders when divided by a third number
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Examples
I certainly believe that our foreign policy is imperial and see such a policy as incongruent with the values of a republic.
But when many states threaten each other for incongruent purposes, who is to do the deterring, and in the face of what provocation?
By now the sound of gun shots rarely distracts me, but this time it was too close, and too incongruent with the bustling nightlife.
In the first, the phylogenies of different genes were shown to be incongruent, indicating recombination between the genes.
Conspicuous consumption of incongruent high-rise real-estate at the expense of venerable neighborhood community centers!
Biogeography and comparative phylogeography differ in their potential to explain incongruent patterns, owing to the disparate time scales.

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