# Helmut Brandl

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 Name Helmut Brandl Member for 7 months Seen May 3 at 1:01 Website Location Age
 Jan6 revised Theorems about endofunctions and closuresadded 2 characters in body Jan5 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 $p.islinear(f) = (\forall x,y. x \in p \land y \in p \Rightarrow x \in y.closed(f) \lor y \in x.closed(f)) \land \lnot p.hascycle(f)$ Jan4 comment Theorems about endofunctions and closuresIf 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. Jan4 awarded ● Commentator Jan4 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. Jan4 awarded ● Teacher Jan3 revised Theorems about endofunctions and closuresadded 83 characters in body Jan3 comment Theorems about endofunctions and closuresYou 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. Jan3 revised Theorems about endofunctions and closuresadded 7 characters in body Jan3 comment Theorems about endofunctions and closuresJust 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. Jan3 revised Theorems about endofunctions and closuresdeleted 10 characters in body; deleted 3 characters in body Jan3 revised Theorems about endofunctions and closuresadded 2 characters in body Jan3 asked Theorems about endofunctions and closures