What is the best property of real numbers?
The most useful property of real numbers is that they contain the limit of all converging sequences (of rationals or real numbers). The “completeness” property. This allows them to be used for roots of rational numbers and for differentiation and integration. Some other properties: Every polynomial of odd degree has at least one real root. There are as many real numbers as there are real numbers between 0 and 1. There are as many real numbers between 0 and 1 as there are pairs of real numbers in the unit square. What’s more, you can even map continuously from the line to the square, so small change in number only moves you a small distance in the square. There are more reals than you can count. Even, and this is the weird thing, even if you could count forever. However you arrange to count them, you will always miss out an infinite number of them. The reals are the ONLY complete ordered Archimedean field. What? A field is a structure with a working plus, minus, times and divide operati
