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Furthermore, (1) and (2) imply that the <i>.ec</i> map is an [[order embedding]] with respect to ≤.
In particular, <i>.ec</i> is [[Injective function|injective]] – different objects have different eigenclasses.
Another consequence of (1
:<i>x</i> ϵ <i>y.ec</i> iff <i>x ≤ y</i>,
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