Timeline for "Family Tree" of Theorems
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 10, 2015 at 14:17 | comment | added | François G. Dorais | @YoavKallus Sorry, I misread your description of the arrows. I guess you mean the equivalences rather than the strict implications. | |
| Jun 9, 2015 at 20:24 | comment | added | Yoav Kallus | Just to clarify, I think the double arrows your are talking about are the double stroked arrows, not the double headed arrows. | |
| Jun 9, 2015 at 20:14 | comment | added | François G. Dorais | @YoavKallus: Double arrows usually mean that the converse implication is known to be false. Dependency is very hard to define rigorously. The connection is that if $A$ really depends on $B$ then it must be that $B$ implies $A$. Otherwise, we could use something strictly weaker than $A$ to prove $B$. (For example, $A \lor B$ could be used instead of $A$.) There doesn't seem to be any other purely mathematical ways of defining "dependency". There are, of course, historical and sociological ways to define dependency that behave differently. | |
| Jun 9, 2015 at 19:14 | comment | added | Yoav Kallus | What does a double-headed arrow mean in one of these diagrams (e.g. rmzoo.math.uconn.edu/wp-content/uploads/sites/841/2014/09/…)? I think what Menachem is asking about is dependencies -- i.e. what statements are used to prove what statements -- not implications. While the question of implications is also fascinating, I think it is orthogonal to the question Menachem was asking. | |
| Jun 9, 2015 at 17:08 | history | answered | François G. Dorais | CC BY-SA 3.0 |