Real Numbers vs Integers

Real Numbers

Real numbers are almost any number we encounter in our everyday life. They include:

• Whole numbers, for example, 0, 1, 2, 3, and 4
• Integers (negative numbers, positive numbers, and zero), for example, -4, -2, 0, 2, and 4
• Rational numbers for example ${\dfrac{3}{4}}$, 0.115, 0.333…, and 2.2
• Irrational numbers, for example, π and √2

However, imaginary (complex) numbers of the form √−i, for example, √−3 and infinity, are not real numbers.

Thus, real numbers are all numbers except imaginary or complex numbers. They are symbolized as ‘R’.

Real numbers represent an ordered set of values shown on a number line with increasing values to the right and decreasing values to the left.

Thus any point on the line could be real numbers.

Integers

Integers include all whole numbers and their corresponding negative numbers. They include:

• All positive numbers {1, 2, 3, 4, 5, 6,…}
• All negative numbers {…−1, −2,−3, −4, -5, -6,…}
• Zero {0}

Together a set of real numbers include:

{…-6, -5,-4,-3, -2, -1, 0, 1, 2, 3, 4, 5, 6 …}

Such numbers are without a fractional or a decimal part and are shown on a number line as:

Thus, the main difference is that all integers are real numbers. However, not all real numbers are integers. The difference can be best understood when represented using a Venn-diagram.