Remark 1

Tag 0BVH, permanent. Cite it as [Bourbaki, Tag 0BVH].

The relations $x \in I, y \in I, xy \in I, yx \in I$ imply

f(xy) = f(x) + f(y) = f(yx),

and hence

yx = xy

since

f

is strictly increasing; in other words, the law induced by the law of composition of

E

on an interval

[0, b]

suitably chosen (e.g., such that

b^2 \leq a

) is commutative.

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

Cited by

Nothing.

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