Statements (54)
| Predicate | Object |
|---|---|
| gptkbp:instance_of |
gptkb:Mathematics
|
| gptkbp:depicts |
the concept of cardinality
|
| gptkbp:example |
a recursive function
a pairing function |
| gptkbp:function |
has been generalized in various ways
can be visualized graphically is used in algorithm analysis is used in coding theory can be computed using integer arithmetic has a unique output for each input pair is a fundamental concept in logic is a subject of academic papers is a topic of research in mathematics is applicable in artificial intelligence is important for data structures is injective and surjective is often referenced in literature on computability is related to combinatorial designs is relevant in theoretical physics is studied in number theory is used in cryptography is used in machine learning algorithms preserves order of pairs is often included in mathematical software libraries |
| gptkbp:has_applications_in |
gptkb:Set
|
| https://www.w3.org/2000/01/rdf-schema#label |
Cantor's pairing function
|
| gptkbp:inversions |
Cantor's unpairing function
|
| gptkbp:is_a_bijection |
between natural numbers and pairs of natural numbers
|
| gptkbp:is_a_foundation_for |
discrete mathematics
|
| gptkbp:is_a_mathematical_construct_that |
simplifies pairwise comparisons
|
| gptkbp:is_a_specific_case_of |
generalized pairing functions
|
| gptkbp:is_a_tool_for |
encoding pairs of data
|
| gptkbp:is_associated_with |
gptkb:Hilbert's_hotel_paradox
|
| gptkbp:is_computable_in |
constant time
|
| gptkbp:is_defined_by |
non-negative integers
(n, m) ↦ (n + m)(n + m + 1)/2 + m |
| gptkbp:is_essential_for |
combinatorial mathematics
|
| gptkbp:is_related_to |
gptkb:Gödel_numbering
Cantor's diagonal argument Cantor's set theory |
| gptkbp:is_represented_in |
a polynomial function
|
| gptkbp:is_symmetric_in |
its arguments
|
| gptkbp:is_taught_in |
mathematics courses
|
| gptkbp:is_used_in |
theoretical computer science
algorithm design |
| gptkbp:is_used_in_proofs_of |
the existence of bijections
|
| gptkbp:is_utilized_in |
database indexing
|
| gptkbp:key_concept |
the study of infinity
|
| gptkbp:map |
pair of natural numbers to a single natural number
|
| gptkbp:named_after |
gptkb:Georg_Cantor
|
| gptkbp:technique |
pairing elements in sets
|
| gptkbp:was_a_demonstration_of |
countability of the Cartesian product of natural numbers
|
| gptkbp:bfsParent |
gptkb:Georg_Cantor
|
| gptkbp:bfsLayer |
4
|