Bourbaki

Exercise 8, § 1

Algebra, VI, p. 31

Let x be an element of an ordered group such that y = inf(x, 0) is defined; if n > 0 is an integer, then nx ≥ 0 implies x ≥ 0 (we' have

ny=inf⁡(nx,(n−1)x,...,0)≥inf⁡((n−1)x,...,0)=(n−1)y; ny = \inf(nx, (n-1)x, ..., 0) \geq \inf((n-1)x, ..., 0) = (n-1)y;

and hence nx = 0 implies x = 0.

Solution

No solution has been written yet.

Transcribed from the printed volume. Not translated.