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. |
: 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. |
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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 '''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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: --[[User:Brnikat|Brnikat]] ([[User talk:Brnikat|talk]]) 21:15, 5 August 2015 (UTC) |
: --[[User:Brnikat|Brnikat]] ([[User talk:Brnikat|talk]]) 21:15, 5 August 2015 (UTC) |
Revision as of 18:10, 6 August 2015
Some thoughts
- We also have: Determine if a string is numeric
- What does integerness mean? would "Have no imaginary part(s) and nothing* after the decimal point" do?
- (At least for ints, reals, complex, and Quaternion types; not sure about infinities and whatnot).
- *Note, .999... === 1 though.
--Paddy3118 (talk) 16:54, 18 June 2014 (UTC)
- An integer is an element of Z. Complex numbers, quaternions etc do no qualify as integers even if their real components are integers. There would be some sense in considering them so, but it's not the case mostly for historical reasons I guess.
- To make the task clearer, I'll add a link to the Wikipedia article. Hope that helps.--Grondilu (talk) 13:50, 21 June 2014 (UTC)
- REXX considers 1.00 and 1e27 to be integers as long as Numeric Digits is large enough. ok? --Walterpachl (talk) 19:12, 21 June 2014 (UTC)
On second thought, the test makes sense with complex numbers. Basically a complex number is an integer if its real part is integer and its imaginary part is nul.--Grondilu (talk) 08:04, 22 June 2014 (UTC)
- (As per above) I'm assuming that 4+0i is an integer, even though the 0i isn't "nul"; the imaginary part is equal to zero, but it's not equal to a "nul" (depending on one's definition of the equality of zero and "nul" in the previous sentence). -- Gerard Schildberger (talk) 15:31, 25 June 2014 (UTC)
- What I meant that zero (0) [or 0i] and "nul" aren't the same thing, they aren't equal. And I wasn't talking about nul as having a value as undefined or somesuch. Also, a nul character ('00x') and a null value are two different animals. [ ] is not equal to [0]. -- Gerard Schildberger (talk) 20:23, 25 June 2014 (UTC)
- "The question is," said Alice, "whether you can make words mean so many different things." ──── Through the Looking-Glass by Lewis Carroll (Charles Lutwidge Dodgson).
- 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 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.
- --Brnikat (talk) 21:15, 5 August 2015 (UTC)