theorem 3.69 Uncountability of the continuum
open in the book ·
parts/02-mathematical-methods/01-logic-sets.tex:1742
· p. 37
Rests on
-
depends_on
definition 3.65
Countable set
¶
- depends_on axiom 3.33 Peano axioms ¶
-
depends_on
definition 3.62
Equipotence
¶
- depends_on definition 3.47 Bijective map ¶
- depends_on definition 3.40 Cardinal ¶
- depends_on definition 3.46 Surjective map ¶
- proves proof ch:01-logic-sets@proof-15 ¶
Supports
- depends_on corollary 3.70 cor:inf-irrationals-uncountable ¶
- depends_on remark 7.94 Three numbers, two kinds ¶
Neighborhood
Every logical edge within two steps of this node.
- declared and complete
- partly declared
- a check failed
- not graded
- declared in the source
- inferred from structure
Edges
| type | direction | node | provenance | where |
|---|---|---|---|---|
cites |
→ | Ueber eine elementare Frage der Mannigfaltigkeitslehre | derived | parts/02-mathematical-methods/01-logic-sets.tex:1744 |
depends_on |
→ | Countable set | declared | parts/02-mathematical-methods/01-logic-sets.tex:1745 |
depends_on |
→ | Surjective map | declared | parts/02-mathematical-methods/01-logic-sets.tex:1745 |
depends_on |
← | cor:inf-irrationals-uncountable | declared | parts/02-mathematical-methods/01-logic-sets.tex:1784 |
depends_on |
← | Three numbers, two kinds | declared | parts/02-mathematical-methods/05-real-analysis.tex:2849 |
proves |
← | ch:01-logic-sets@proof-15 | declared | parts/02-mathematical-methods/01-logic-sets.tex:1748 |