SEARCH HOME
 Math Central Quandaries & Queries
 Question from Ghani: Hello, 1. Are set partition "sets"? 2. If they are so then, why are both {{a}{b,c}} and {{a,b}{c}} said to be valid partitions of A ={a,b,c} despite them having different elements? (I understand that set are equal if they have the exact same elements). Thank you!

Hi,

A partition of a set is a collection of non-empty subsets of the set such that every element of the set is in at least one of the subsets and no element of the set is in more than one of the subsets.

You have written partitions of the set $A$ as sets which is certainly valid. {{a},{b,c}} is a partition of $A$ as are {{a,b},{c}}, {{a,c},{b}}, {{a},{b},{c}} and {{a,b,c}}. There are exactly 5 partitions of a set with 3 elements.

Harley

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.