|

# number

## The Real Numbers

The real numbers are those representable by an infinite decimal expansion, which may be repeating or nonrepeating; they are in a one-to-one correspondence with the points on a straight line and are sometimes referred to as the continuum. Real numbers that have a nonrepeating decimal expansion are called irrational, i.e., they cannot be represented by any ratio of integers. The Greeks knew of the existence of irrational numbers through geometry; e.g., 2 is the length of the diagonal of a unit square. The proof that 2 is unable to be represented by such a ratio was the first proof of the existence of irrational numbers, and it caused tremendous upheaval in the mathematical thinking of that time.

#### More on number The Real Numbers from Infoplease:

• number: The Real Numbers - The Real Numbers The real numbers are those representable by an infinite decimal expansion, which ...
• real number - real number: real number: see number.
• number - number number, entity describing the magnitude or position of a mathematical object or extensions ...
• ring, mathematical system - ring ring, in mathematics, system consisting of a set R of elements and two binary operations, such ...
• Encyclopedia: Mathematics - Encyclopeadia articles concerning Mathematics.

#### See more Encyclopedia articles on: Mathematics

Related content from HighBeam Research on: number: The Real Numbers

# 24 X 7

## Private Tutor

 24 x 7 Tutor Availability Unlimited Online Tutoring 1-on-1 Tutoring