Algebra: Number Systems

Number Systems

In this math video tutorial, we introduce several of the basic number sets used in mathematics: Natural Numbers, Whole Numbers, Integers, Rational Numbers, and Real Numbers. By far the most common of these is the Real Numbers, which is what we will typically use for all of our math videos.

Despite this, each of these number systems introduces new properties that we will use when solving math problems in the real numbers. For this reason, we have chosen to give a concrete demonstration of how these properties generate their associated number sets.

These properties are closure, identity, and inverses under addition and multiplication. The Natural Numbers, N, are closed under addition and multiplication and contain the multiplicative identity element 1. The Whole Numbers, W, add an additive identity element to that. Additive inverses are included with the set of Integers, Z. The Rational Numbers, Q, add multiplicative inverses for all nonzero elements. Finally, the Real Numbers, R, add the remaining elements to the number line.

Although it is not obvious, not all real numbers are rational. Real numbers, which are not rational, are called irrational. Two of the most common irrational numbers are square root of 2 and ?. These numbers are found in the diagonal of a square with side length 1 and the circumference of a circle of radius one-half, respectively.