Talk:Test integerness: Difference between revisions
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:: --[[User:Paddy3118|Paddy3118]] ([[User talk:Paddy3118|talk]]) 16:11, 25 June 2014 (UTC) |
:: --[[User:Paddy3118|Paddy3118]] ([[User talk:Paddy3118|talk]]) 16:11, 25 June 2014 (UTC) |
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: Mathematicians define a complex number (an element of the field '''C''') as an ordered pair |
: Mathematicians define a complex number (an element of the field '''C''') as an ordered pair (''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. |
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: 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. |
: 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. |
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