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Revision difference : property
Version 6 Version 5
Given any element of a set $X$, a certain property $p$ is either true or false. Formally, a property $p$ is a function $p\colon X \to \{\mathit{true},\mathit{false}\}$. Any property gives rise in a natural way to the set $\{x\in X : x\text{ has the property }p\}$ and the corresponding \PMlinkid{characteristic function}{CharacteristicFunction}. Given any element of a set $X$, a certain property $p$ is either true or false. Formally, a property $p$ is a function $p\colon X \to \{\mathit{true},\mathit{false}\}$. Any property gives rise in a natural way to the set $\{x: x\text{ has the property }p\}$ and the corresponding \PMlinkid{characteristic function}{CharacteristicFunction}.
Using only elements of some set $X$ to define the new set is done to avoid Russell's paradox.