User:IssaRice/Analogous results between subfields of math: Difference between revisions
(Created page with " ==See also== * https://machinelearning.subwiki.org/wiki/User:IssaRice/Subfield_of_math_as_study_of_concepts_preserved_under_transformation") |
No edit summary |
||
| Line 1: | Line 1: | ||
==Injective iff surjective== | |||
* If A and B are finite sets that have the same cardinality, then <math>f: A \to B</math> is injective iff surjective. | |||
* If V and W are finite-dimensional vector spaces with the same dimension, then a linear map <math>T : V \to W</math> is injective iff surjective. | |||
==See also== | ==See also== | ||
* https://machinelearning.subwiki.org/wiki/User:IssaRice/Subfield_of_math_as_study_of_concepts_preserved_under_transformation | * https://machinelearning.subwiki.org/wiki/User:IssaRice/Subfield_of_math_as_study_of_concepts_preserved_under_transformation | ||
Revision as of 20:38, 29 August 2020
Injective iff surjective
- If A and B are finite sets that have the same cardinality, then is injective iff surjective.
- If V and W are finite-dimensional vector spaces with the same dimension, then a linear map is injective iff surjective.
