Set Definition by Predicate/Examples/Musical Mathematicians
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Example of Set Definition by Predicate
Let $M$ denote the set of all the mathematicians in the world.
Let $I$ denote the set of all people who can play a musical instrument.
Let $S$ denote the set of all mathematicians who can play a musical instrument.
Then we can define $S$ as:
- $S := \set {x: x \in M \text { and } x \in I}$
or as:
- $S := \set {x \in M: x \in I}$
Sources
- 1975: T.S. Blyth: Set Theory and Abstract Algebra ... (previous) ... (next): $\S 1$. Sets; inclusion; intersection; union; complementation; number systems