tag:blogger.com,1999:blog-2715968472735546962.post2279751171207911172..comments2023-12-14T02:21:18.222+01:00Comments on Bannalia: trivial notes on themes diverse: A relationship on real functionsJoaquín M López Muñozhttp://www.blogger.com/profile/08579853272674211100noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-2715968472735546962.post-1984617904354227362014-01-10T03:43:18.221+01:002014-01-10T03:43:18.221+01:00Hi, actually gmax(x) =max{g(y) : y ≤ x}=max{y : y ...Hi, actually gmax(x) =max{g(y) : y ≤ x}=max{y : y ≤ x}=x, not infinity. Note the ≤ in the definition of gmax.Joaquín M López Muñozhttps://www.blogger.com/profile/08579853272674211100noreply@blogger.comtag:blogger.com,1999:blog-2715968472735546962.post-22149462164176968092014-01-09T20:55:45.396+01:002014-01-09T20:55:45.396+01:00Proposition 2 might not hold true in both directio...Proposition 2 might not hold true in both directions.<br /><br />Consider<br />f := x + 2<br />g := x<br /><br />Clearly, f >> g with h := x + 1<br /><br />But from<br />fmin = f<br />gmax = infinity<br />follows that <br />fmin(x) < gmax(x) for some x<br /><br />which contradicts<br />(f >> g) => (fmin(x) > gmax(x))<br />abehttps://www.blogger.com/profile/11265886114680193003noreply@blogger.comtag:blogger.com,1999:blog-2715968472735546962.post-26398227480827516122014-01-09T20:54:51.087+01:002014-01-09T20:54:51.087+01:00Proposition 2 might not hold true in both directio...Proposition 2 might not hold true in both directions.<br /><br />Consider<br />f := x + 2<br />g := x<br /><br />Clearly, f >> g with h := x + 1<br /><br />But from<br />fmin = f<br />gmax = infinity<br />follows that <br />fmin(x) < gmax(x) for some x<br /><br />which contradicts<br />(f >> g) => (fmin(x) > gmax(x))<br />nonsequiturhttps://www.blogger.com/profile/17387581570831324910noreply@blogger.com