Talk:Smallest Element is Initial Object

This definition presupposes that a poset does have a smallest element. Example: $\{\{a\}, \{b\}, \{a, b\}\}$ under the subset ordering has two minimal objects, but no smallest. So if a poset has no smallest element, it has no initial object? --prime mover (talk) 18:47, 29 August 2012 (UTC)

This is correct. E.g. $(\Z, \le)$ does not have an initial object. Mind you, it is a theorem, not a definition. I'll adapt the wording to try and make this clearer. --Lord_Farin (talk) 20:55, 29 August 2012 (UTC)