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The formal statement of the theorem derives an expression for the physical quantity that is conserved (and hence also defines it), from the condition of invariance alone. For example:
* the invariance of physical systems with respect to [[translation (physics)|translation]] (when simply stated, it is just that the laws of physics don't vary with ___location in space) translates into the law of conservation of [[linear momentum]];
* invariance with respect to [[rotation]] gives law of conservation of [[angular momentum]];
* invariance with respect to [[time]] gives the well known [[law of conservation of energy]], et cetera.
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