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How to prove this? I understand monotonicity implies local non-satiation but does strongly monotone also imply it? How to prove it like this - https://felixmunozgarcia.files.wordpress.com/2017/08/recitation_1.pdf (page 4 answer(b))?

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    $\begingroup$ Yes because Strong monotonicity implies monotonicity. $\endgroup$
    – Amit
    Oct 7, 2022 at 14:49

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Yes. Suppose not, then there exists some $x \in X, \varepsilon > 0$ such that $u(x) > u(x') \; \forall \;x' : \|x - x'\| < \varepsilon$, which is the definition of a local maximum and contradicts strict monotonicity.

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