Local nonsatiation

The property of local nonsatiation of consumer preferences states that for any bundle of goods there is always another bundle of goods arbitrarily close that is preferred to it. What this means is that a consumer always either prefers more of an item or less of an item, never a particular amount of a good. An additional requirement is that there is some good that consumer does prefer more of.

Formally if X is the consumption set, then for any ${\displaystyle x\in X}$ and every ${\displaystyle \varepsilon >0}$, there exists a ${\displaystyle y\in X}$ such that ${\displaystyle \|y-x\|\leq \varepsilon }$ and ${\displaystyle y}$ is preferred to ${\displaystyle x}$.

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