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. |
What do we want to do, Wikipedians?
''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.
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.