Talk:Test integerness: Difference between revisions

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: Mathematicians define a complex number (an element of the field '''C''') as an ordered pair of elements (''re'', ''im'') where ''re'' and ''im'' are elements of the field '''R''', the real numbers. An ordered pair of elements is quite distinct from a single element.

: If you wish to test whether a complex number is an integer you also need to be careful to state what you mean by that term. A complex integer, more usually termed a ''Gaussian integer'' or '''Z'''[''i''], is an ordered pair of elements (''re'', ''im'') of the ring '''Z''', the ring of integers. The sub-ring which has ''im'' = 0 is isomorphic to '''Z'''. My ''guess'' is that the latter set is what is meant when the task is extended to treat complex numbers but this should be made explicit.

: If you wish to test whether a complex number is an integer you also need to be careful to state what you mean by that term. A complex integer, more usually termed a ''Gaussian integer'' or an element of the ring '''Z'''[''i''], is an ordered pair of elements (''re'', ''im'') of the ring '''Z''', the ring of integers. The sub-ring which has ''im'' = 0 is isomorphic to '''Z'''. My ''guess'' is that the latter set is what is meant when the task is extended to treat complex numbers but this should be made explicit.

: --[[User:Brnikat|Brnikat]] ([[User talk:Brnikat|talk]]) 21:15, 5 August 2015 (UTC)