if a number is the successor of another number, then the first number is said to be "larger than" the other number. if a number is larger than another number, and if the other number is larger than a third number, then the first number is also larger than the third number. example: five is larger than four, and four is larger than three, therefore five is larger than three. but six is larger than five, therefore six is also larger than three. but seven is larger than six, therefore seven is also larger than three ... therefore eight is larger than three ... therefore nine is larger than three, etc.