could anyone please let me know the correct reading(sentence form) of set builder notation, confused with different interpretation in different resources.
Many Thanks
could anyone please let me know the correct reading(sentence form) of set builder notation, confused with different interpretation in different resources.
Many Thanks
The set $\{x\mid\varphi(x)\}$ is "The set of all $x$ such that $\varphi(x)$ holds." Note that sometimes such collection is not a set (e.g. the collection of all sets); and sometimes we wish to limit the elements to be taken from a certain set $A$.
The set $\{x\in A\mid\varphi(x)\}$ is "The set of all $x$ in $A$ such that $\varphi(x)$ is true."