Helmut Brandl
|
Registered User
|
|
|
Jan 6 |
revised |
Theorems about endofunctions and closures added 2 characters in body |
|
Jan 5 |
comment |
Theorems about endofunctions and closures @Joel: I think you are right with your comment on "islinear". My definition seems to be too restrictive. Maybe it is better to use $p.islinear(f) = (\forall x,y. x \in p \land y \in p \Rightarrow x \in y.closed(f) \lor y \in x.closed(f)) \land \lnot p.hascycle(f)$ |
|
Jan 4 |
comment |
Theorems about endofunctions and closures If both of these implications are easy to prove, why don't you provide a proof. My problems is that I have not yet been able to prove these implications. They are evident, but I need a proof. |
|
Jan 4 |
awarded | ● Commentator |
|
Jan 4 |
comment |
Theorems about endofunctions and closures @Joel Notation: How would you write these predicates? $cyc(p,f)$ and $lin(p,f)$? Integers: I am looking only at closures here(my intention is to prove assertions of linked structures). The predicate $p.islinear(f)$ expresses the fact that $p$ is a closure starting from a one element set and does not have cycles. The fact that the set of integers is not linear according to this definition is implied by the fact that the integers are not a closure under a function starting from a one element set. |
|
Jan 4 |
awarded | ● Teacher |
|
Jan 3 |
revised |
Theorems about endofunctions and closures added 83 characters in body |
|
Jan 3 |
comment |
Theorems about endofunctions and closures You are right again. I have transcribed it wrongly into latex. The clause $p=a.closed(f)$ substitutes the clause $a \in p$ because the former implies the latter. |
|
Jan 3 |
revised |
Theorems about endofunctions and closures added 7 characters in body |
|
Jan 3 |
comment |
Theorems about endofunctions and closures Just the opposite. Starting from $f(a)$ and repeatedly applying $f$ it cycles back to $a$. This was a typo which I have corrected now. Sorry and thanks for the hint. |
|
Jan 3 |
revised |
Theorems about endofunctions and closures deleted 10 characters in body; deleted 3 characters in body |
|
Jan 3 |
revised |
Theorems about endofunctions and closures added 2 characters in body |
|
Jan 3 |
asked | Theorems about endofunctions and closures |
