How Many Numbers Are There?

[wurlycorner]

I had a recollection about there being real numbers, so I looked them up to remind myself what they were...

In mathematics, a real number is a value that represents a quantity along a continuous line. The real numbers include all the rational numbers, such as the integer −5 and the fraction 4/3, and all the irrational numbers such as √2 (1.41421356… the square root of two, an irrational algebraic number) and π (3.14159265…, a transcendental number). Real numbers can be thought of as points on an infinitely long line called the number line or real line, where the points corresponding to integers are equally spaced. Any real number can be determined by a possibly infinite decimal representation such as that of 8.632, where each consecutive digit is measured in units one tenth the size of the previous one. The real line can be thought of as a part of the complex plane, and correspondingly, complex numbers include real numbers as a special case.

Riiiiigggghhhhhtttt... Ok then, so that just about covers it then?


But wait, the very next line it then says says:

These descriptions of the real numbers are not sufficiently rigorous by the modern standards of pure mathematics

[CrunchyAdams82]

Simples!

[andypont]

Infinite.
The fact that 10 individual digits are used to make up other numbers is irrelevant.

By that logic most of us drive cars with h22 engines, does that mean there are only a few (h22a, a5 a8 etc) rather than each car having its own and therefore thousands existing?

I know that's taking the point to the extreme, but the logic works in my mind at least!!