Statements (59)
| Predicate | Object |
|---|---|
| gptkbp:instance_of |
gptkb:Mathematics
|
| gptkbp:allows |
the completion of the rational numbers
|
| gptkbp:consists_of |
two non-empty sets
|
| https://www.w3.org/2000/01/rdf-schema#label |
Dedekind cuts
|
| gptkbp:is_a |
gptkb:software_framework
gptkb:Data_Analytics theoretical construct concept in mathematical logic concept in set theory method of analysis theoretical construct in mathematics constructive approach constructive method method of constructing real numbers from rationals method of defining continuity in analysis method of defining numbers method of defining real numbers method of number construction theoretical framework for numbers |
| gptkbp:is_applied_in |
gptkb:analysis
number theory |
| gptkbp:is_compared_to |
Cauchy sequences
|
| gptkbp:is_connected_to |
the history of mathematics
|
| gptkbp:is_considered_as |
a rigorous approach to real numbers
|
| gptkbp:is_defined_by |
a method of constructing real numbers
|
| gptkbp:is_described_as |
mathematical literature
|
| gptkbp:is_essential_for |
mathematical education
the study of functions |
| gptkbp:is_fundamental_to |
the concept of limits
the understanding of irrational numbers the understanding of real numbers |
| gptkbp:is_part_of |
the study of real analysis
the foundation of real numbers |
| gptkbp:is_related_to |
gptkb:Set
the completeness property of real numbers the concept of completeness in mathematics the concept of density in real numbers the concept of intervals the concept of rational numbers the concept of supremum |
| gptkbp:is_represented_in |
a pair of sets
|
| gptkbp:is_used_for |
defining limits and convergence
|
| gptkbp:is_used_in |
mathematical proofs
theoretical mathematics the development of calculus the analysis of functions the construction of the real line the study of limits and continuity |
| gptkbp:is_used_to |
define continuity
define the real number line define the real number system establish the properties of real numbers prove the existence of limits |
| gptkbp:named_after |
gptkb:Richard_Dedekind
|
| gptkbp:provides |
a way to define irrational numbers
|
| gptkbp:satisfies |
certain properties of order
|
| gptkbp:used_in |
real analysis
|
| gptkbp:bfsParent |
gptkb:Richard_Dedekind
|
| gptkbp:bfsLayer |
5
|