Readings for Session 3 – (Continued)
Verbal, Roster, and Set-builder Notation for a Set:
We have three ways of
describing sets:
1.
by name or verbal description of the
elements of a set,
Example:
Let S represent the
collection of states that border Minnesota (verbal)
S = {North Dakota, South Dakota, Iowa, Wisconsin, Michigan}
(roster)
S = {x : x is a state bordering
Minnesota} (set-builder)
The set-builder form is read as “S
is the set of all x
such that x is a state
bordering Minnesota.”
Example:
Let
N represent the
collection of counting numbers (verbal)
N = {1, 2, 3, 4, …} (roster)
N = {x :
x is a counting number} (set-builder)
Example:
The set of presidents of the U.S. who were still alive
June 15, 2009 (verbal)
{Jimmy Carter, George H. W. Bush, Bill Clinton, George W. Bush,
Barack Obama} (roster)
{x :
x was a President of the U.S. who was still alive June 15, 2009} (set-builder)
The set-builder form is read, “the
set of all objects such that the object was a president of the
U.S. who was still alive June 15, 2009.”
Example:
The counting number multiples of 5 that are less than 30
(verbal)
{5, 10, 15, 20, 25} (roster)
{x :
x is a counting number multiple of 5 that is less than 30} (set-builder)
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