Wikipedia: Real number/Talk

"Real numbers" has just been redirected to "Real number". Fine with me, but presently "Rational number" redirects to "Rational number".

What do we want to do, Wikipedians?

Thanks for noticing that "rational number" has the same problem--it's fixed now. The singular form is preferred for simple nouns like this to make linking easier. For example, "...probability can be expressed as a real number in the interval [0,1]..." --LDC

''A real number is one that can be expressed in the form 'DDD.ddd'. DDD is zero or more decimal digits ddd is zero or more decimal digits Of course, DDD must be finite in length. This restriction does not apply to ddd.''

Why must DDD be finite in length? If a sequence of real numbers goes to infinity, then there must be an (countably) infinite number of digits in ...DDD. What am I missing?

I don't really understand the question. The sequence 10¹,10²,10³,10⁴,... goes to infinity, but none of the numbers have infinite digits.

In effect, a sequence of numbers may go to infinity, but a single number can't. (Consider the problem of comparing two such "infinite integers". How could you decide which was bigger without calculating all the (infinite) digits ..DDDD for both numbers.

Article says:

: If we have a space where Cauchy sequences are meaningful (a
: metric space, i.e. a space where distance is defined), a
: standard procedure to force all Cauchy sequences to converge is
: adding new points to the space (a process called completing?).
: When applied to the rational numbers, it gives the following
: useful [construction of the real numbers]?:

It should point out that this only works with a Euclidean metric or one equivalent to a Euclidean metric; using other metrics gives you the p-adic numbers instead.

The following comment was moved from the main page:

RB: The dimension is actually difficult to define: the reals have dimension 1 for pretty much any sensible definition, but the best definition I know is that cohomology with compact support is non trivial in dimension 1 and vanishes above it.