Statements (49)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
mathematical set
|
| gptkbp:basisFor |
field theory
|
| gptkbp:cardinality |
aleph_0
|
| gptkbp:characteristic |
0
|
| gptkbp:closed |
addition
multiplication subtraction division (except by zero) |
| gptkbp:completionLeadsTo |
the real numbers R
the p-adic numbers Q_p |
| gptkbp:contains |
0
1 -1 all integers all fractions of integers with nonzero denominator |
| gptkbp:countable |
true
|
| gptkbp:defines |
set of numbers that can be expressed as a fraction a/b where a and b are integers and b ≠ 0
|
| gptkbp:denseIn |
the real numbers R
|
| gptkbp:everyElement |
can be written as a terminating or repeating decimal
|
| gptkbp:field |
true
|
| gptkbp:hasNo |
infinitesimal elements
|
| gptkbp:hasSubgroup |
the real numbers R
the integers Z the natural numbers N |
| gptkbp:heldBy |
infinite set
not algebraically closed Archimedean field a commutative ring a principal ideal domain a simple field extension of the integers a unique factorization domain a vector space over itself not a complete metric space not closed under taking cube roots not closed under taking square roots not complete with respect to the usual metric ordered field subfield of the real numbers the smallest field containing the integers not closed under taking limits of all Cauchy sequences |
| https://www.w3.org/2000/01/rdf-schema#label |
the rational numbers Q
|
| gptkbp:notComplete |
true
|
| gptkbp:primeFieldOf |
characteristic 0 fields
|
| gptkbp:symbol |
gptkb:Q
|
| gptkbp:usedIn |
gptkb:algebra
analysis number theory |
| gptkbp:bfsParent |
gptkb:the_ring_of_integers_Z
|
| gptkbp:bfsLayer |
7
|