A set
in a first-countable space is dense in if , where is the set of limit points of . For example, the rational numbers are dense in the reals.
In general, a subset of
is dense if its set closure.
A real number
is said to be -dense
iff, in the base- expansion of , every possible finite string of consecutive digits appears.
If is -normal, then is also -dense. If, for some ,
is -dense, then is irrational. Finally, is -dense
iff the sequence is dense (Bailey and Crandall 2001, 2003).
Bailey, D. H. and Crandall, R. E. "On the Random Character of Fundamental Constant Expansions." Exper. Math.10,
175-190, 2001.Bailey, D. H. and Crandall, R. E. "Random
Generators and Normal Numbers." Exper. Math.11, 527-546, 2002.
in a first-countable space is dense in 
if 
, where 
is the set of limit points of 
. For example, the rational numbers are dense in the reals.
In general, a subset 
of 
is dense if its set closure 
.
is said to be 
-dense
iff, in the base-
expansion of 
, every possible finite string of consecutive digits appears.
If 
is 
-normal, then 
is also 
-dense. If, for some 
, 
is 
-dense, then 
is irrational. Finally, 
is 
-dense
iff the sequence 
is dense (Bailey and Crandall 2001, 2003).
