"We sometimes use curly brace notation in combination with a colon to define a set intensionally. Consider this: M = {k : k is between 1 and 20, and a multiple of 3}. When you reach a colon, pronounce it as “such that.” So this says “M is the set of all numbers k such that k is between 1 and 20, and a multiple of 3.” This is an intensional definition, since we haven’t listed the specific numbers in the set, but rather given a rule for finding them. Another way to specify this set would be to write M = {3, 6, 9, 12, 15, 18}, which is an extensional definition of the same set. Increasing the intension decreases the extension. For example, suppose F is initially defined as the set of all females in the Davies family. Now suppose I decide to add to that intension by making it the set of all adult females. By adding to the intension, I have now reduced the extension from {Mom, Lizzy, Marina} to just {Mom}. The reverse is true as well: trimming down the intension by removing conditions effectively increases the extension of the set. Changing “all female persons” to just “all persons” includes Dad and T.J. in the mix."