Cantor's continuum hypothesis
GPTKB entity
Statements (58)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:physicist
|
| gptkbp:designedBy |
there is no set whose cardinality is strictly between that of the integers and the real numbers
|
| gptkbp:explores |
the continuum hypothesis
|
| gptkbp:first_held |
1878
|
| gptkbp:has_a_focus_on |
philosophy of mathematics
|
| gptkbp:has_implications_for |
the size of infinite sets
the nature of mathematical objects the understanding of infinity the nature of mathematical infinity the understanding of set sizes |
| https://www.w3.org/2000/01/rdf-schema#label |
Cantor's continuum hypothesis
|
| gptkbp:independence |
gptkb:Zermelo-Fraenkel_set_theory_with_the_Axiom_of_Choice_(ZFC)
|
| gptkbp:involves |
the real number line
|
| gptkbp:is_a |
cardinal numbers
debated for over a century analyzed in various mathematical frameworks debated in mathematical circles examined by mathematicians worldwide the continuum of real numbers the focus of many mathematical papers the size of the continuum the subject of many mathematical discussions |
| gptkbp:is_a_center_for |
the philosophy of mathematics
|
| gptkbp:is_a_dish_that |
the existence of certain types of sets
|
| gptkbp:is_a_subject_of |
mathematics
set theory academic research mathematical logic mathematical research philosophical debate foundational mathematics the study of infinite sets mathematical exploration mathematical seminars intense mathematical scrutiny mathematical lectures mathematical inquiry mathematical discussion the study of set theory |
| gptkbp:is_designed_to |
gptkb:Georg_Cantor
|
| gptkbp:is_displayed_on |
independent of the standard axioms of set theory
|
| gptkbp:is_essential_for |
the history of mathematics
the study of cardinality |
| gptkbp:is_linked_to |
the concept of bijection
|
| gptkbp:is_popular_among |
CH
|
| gptkbp:is_studied_in |
the Axiom of Choice
many mathematicians |
| gptkbp:is_used_in |
infinity
mathematical logic discussions of infinity the field of mathematics |
| gptkbp:isConnectedTo |
gptkb:Cantor's_theorem
|
| gptkbp:related_to |
set theory
the concept of cardinality the concept of continuum |
| gptkbp:significantEvent |
the philosophy of mathematics.
|
| gptkbp:suitableFor |
major unsolved problem in mathematics
|
| gptkbp:was_a_result_of |
consistent with ZFC
|