Statements (21)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
real number
|
| gptkbp:cardinality |
continuum
|
| gptkbp:category |
dense in real numbers
set of measure zero |
| gptkbp:defines |
A real number x such that for every positive integer n, there exist integers p and q > 1 with |x - p/q| < 1/q^n.
|
| gptkbp:example |
gptkb:Liouville_constant
|
| gptkbp:firstProvedTranscendental |
1844
|
| gptkbp:hasSubgroup |
transcendental numbers
|
| gptkbp:heldBy |
irrational number
uncountable not algebraic number number with very good rational approximations transcendental number |
| https://www.w3.org/2000/01/rdf-schema#label |
Liouville number
|
| gptkbp:measures |
zero (Lebesgue measure)
|
| gptkbp:namedAfter |
gptkb:Joseph_Liouville
|
| gptkbp:notSubsetOf |
algebraic numbers
|
| gptkbp:property |
not all transcendental numbers are Liouville numbers
every Liouville number is transcendental |
| gptkbp:bfsParent |
gptkb:Joseph_Liouville
|
| gptkbp:bfsLayer |
6
|