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The two notions are related.
One should not blend the two notions.
Then, in 1999, a centre-left government added the two notions together.
An Introduction to the Logic of the Two Notions" (Cornell UP, 1962).
So although the two notions have quite different usages, they are very related.
And also, as we go along, exploit the two notions together.
That close association doesn't mean the distinction between the two notions is specious.
The two notions coincide, however, whenever the latter is maximal monotone.
However, in spite of this similarity the two notions do not coincide.
Hence the equivalence of the two notions in (1) follows by combining Lemma 23.8.3 with Algebra, Lemma 10.133.7.
There are special cases, where the two notions of power are strictly proportional and, therefore, no conflict occurs.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com