Talk:Test integerness

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)

Thanks for clarifying the task. --Paddy3118 (talk) 12:11, 21 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)

I'm not sure I understand the problem. 1.00 and 1e27 *are* integers. They may be stored as floating point numbers, but they are integers.--Grondilu (talk) 01:11, 22 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)

I wonder what you mean by «0i isn't nul». It is very much nul to me, or equal to zero, which means the same imho. Unless you're talking about nul as "undefined" or something, but that's clearly not what we're talking about here.--Grondilu (talk) 19:46, 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).

Well, we were talking about numbers, not characters or anything. So in that context nul does mean zero imho.--Grondilu (talk) 11:19, 26 June 2014 (UTC)

Imaginary numbers are taught as existing on an orthogonal axis to the reals intersecting the reals at 0j. It seems OK to thing of am imaginary number with zero imaginary part and zero after the decimal point as equivalent to an integer for this task.

--Paddy3118 (talk) 16:11, 25 June 2014 (UTC)

Mathematicians define a complex number (an element of C) as an ordered pair of elements (re, im) where re and im are elements of 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], the Gaussian integers is an ordered pair of elements (re, im) of Z, the integers. The subset 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)