Assertion: real number | /r/HasProperty | normal
Facets:
value: in one base
type: LOCATION
value: in mathematics
type: OTHER
value: simply
type: DEGREE
value: in an integer base b
type: OTHER
Source sentences:
text: In mathematics, a real number is said to be simply normal in an integer base b  if its infinite sequence of digits is distributed uniformly in the sense that each of the b digit values has the same natural density 1/ b .
text: While a general proof can be given that almost all real numbers are normal, by proving the set of non-normal numbers has Lebesgue measure zero, this proof is not constructive, and only a few specific numbers have been shown to be normal.
text: A given infinite sequence is either normal or not normal, whereas a real number, having a different base-b expansion for each integer b ≥ 2, may be normal in one base but not in another (in which case it is not a normal number).
text: Using the Borel–Cantelli lemma, he proved that almost all real numbers are normal, establishing the existence of normal numbers.