It is assumed in what follows that the reader knows enough mathematics to understand the distinction between
1. The integers:
0, 1, -1, 2, -2, 3, -3, etc.The ratios (with numerators and denominators):
1/2, -1/2, 1/3, -1/3, 2/3, -2/3, 3/4 etc.Floating point numbers:
0.135, 1.35, 13.5 -0.135, -1.35, etc.Complex numbers with real and imaginary parts, such as the square root of -1.
It is also assumed that readers know that floating point numbers can be represented as manitissa and exponent, and will therefore understand what is printed out by the following, where each number in the first row is represented as <mantissa>e<exponent>:
1.234e4, 1.234e3, 1.234e2, 1.234e1, 1.234e0, 1.234e-1, 1.234e-2 => ** 12340.0 1234.0 123.4 12.34 1.234 0.1234 0.01234(Extra spaces have been inserted in the printout, to simplify comparisons.)
Readers who do not know all about these topics may nevertheless be able to pick up the information from the explanations given below. Alternatively they can omit sections on unfamiliar kinds of numbers, e.g. complex numbers.
Note: in Pop-11 complex numbers have real and imaginary parts that themselves can be integral (i.e. positive or negative integers) or ratios, or floating point numbers, or any combination of these.