

Real numbers are numbers that can take a positive, negative, or zero value. For example:
400, 20, 11.75, 3, 0, +1, +3.76, +1000
Integers are whole numbers, positive or negative, that have no fractional parts. For example:
400, 20, 11, 3, 0, +1, +3, +1000
Rational numbers are fractional numbers and may be positive or negative. Rational numbers include fractions that are less than one, those that are greater than one (socalled improper fractions). Formally stated, rational numbers have the form a/b, where a and b are integers, b cannot be zero, and there are no common factors (i.e., 4/6 should be reduced to 2/3). Note that b can equal 1, so all integers, including zero, can be seen as rational numbers with a value of b equal to 1. For example:
7/2, 1/4, 0/1, +1/8, +1/4, +3/2, +16/1
Irrational numbers are a form of rational numbers where a and b are noninteger. Irrational numbers can be produced in a number of ways; for example, π is irrational, and the square root of any prime number is irrational (e.g., √2 or √13). For example:
2.2360679, 3.1415926
A Prime number is a whole number that is greater than 1 and has no common factors other than 1 and itself (i.e., it cannot be divided by two integers that are greater than 1). Every natural number greater than 1 is either prime or can be expressed as a product of primes (e.g., 28 = 2 × 2 × 7). Prime numbers have many useful applications in cryptography, as discussed in Chapter 15. Examples include:
2, 3, ..., 17, 19, 23, ..., 47, ..., 101, ..., 1093,
Infinity is itself not a number. In effect, it is an unbounded value; we may therefore use the phrase infinitely large or infinitely small to represent inconceivably large or small values respectively. The term infinitesimal means a value whose limit is zero. Infinity is normally represented by the symbol ∞.

