proposition 3.48 Characterization of bijectivity
open in the book ·
parts/02-mathematical-methods/01-logic-sets.tex:1291
· p. 32
Rests on
- depends_on definition 3.47 Bijective map ¶
- depends_on definition 3.45 Injective map ¶
- depends_on definition 3.46 Surjective map ¶
- proves proof ch:01-logic-sets@proof-7 ¶
Supports
-
depends_on
proposition 3.57
Composition of bijective maps
¶
- depends_on proposition 3.63 prop:inf-equipotence-equivalence ¶
-
depends_on
theorem A.1
Cantor–Schröder–Bernstein
¶
- depends_on corollary A.3 The continuum is the power set of the naturals ¶
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 |
|---|---|---|---|---|
depends_on |
→ | Bijective map | declared | parts/02-mathematical-methods/01-logic-sets.tex:1294 |
depends_on |
→ | Injective map | declared | parts/02-mathematical-methods/01-logic-sets.tex:1294 |
depends_on |
→ | Surjective map | declared | parts/02-mathematical-methods/01-logic-sets.tex:1294 |
depends_on |
← | Composition of bijective maps | declared | parts/02-mathematical-methods/01-logic-sets.tex:1435 |
depends_on |
← | Cantor–Schröder–Bernstein | declared | appendices/A-long-proofs.tex:1354 |
proves |
← | ch:01-logic-sets@proof-7 | declared | parts/02-mathematical-methods/01-logic-sets.tex:1297 |