Invariant (mathematics)

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In mathematics, an invariant is something that does not change under a set of transformations. The property of being an invariant is invariance.

Mathematicians say that a quantity is invariant "under" a transformation; some economists say it is invariant "to" a transformation.

One simple example of invariance is that the distance between two points on a number line is not changed by adding the same quantity to both numbers. On the other hand multiplication does not have this property so distance is not invariant under multiplication. Some more complicated examples:

See also