Readings for Session 12 – (Continued)  

Even and Odd Numbers

Even and Odd Numbers: A natural number (whole number) is an even number if it is a multiple of two. A natural number (whole number) that is not an even number is an odd number.

General Property:

A value of the form 2n, where n is a counting number (whole number), is an even number.
A value in the form of 2n – 1 where n is a counting number is an odd number.
A value in the form of 2n + 1 where n is a whole number is an odd number.

Note that an odd number is always one less (or one more) than some even number, 2n.

Set-Builder Notation:

The set of even counting numbers is {x : x = 2n where n ∈ N}.
The set of odd counting numbers is {x : x = 2n – 1 where n ∈ N}.
The set of even whole numbers is {x : x = 2n where n ∈ W}.
The set of odd whole numbers is {x : x = 2n + 1 where n ∈ W}.

Roster Notation:

The set of even counting numbers is {2, 4, 6, 8, 10, …}.
The set of odd counting numbers is {1, 3, 5, 7, 9, …}.
The set of even whole numbers is {0, 2, 4, 6, 8, 10, …}.
The set of odd whole numbers is {1, 3, 5, 7, 9, …}.

Some Other Factor Facts

A counting number that ends in an even digit is an even number.

A counting number that ends in the digit 5 or 0 has 5 as a factor.

A counting number that ends in the digit 0 has 10 as a factor.

A counting number that ends in two zeros has 100 is a factor.

 

      

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