Re: how

Am 24.04.2024 um 22:38 schrieb Chris M. Thomasson:

Then I can say that (XYZ) + .5 is "inside" an interval, but its not representational wrt 0, 1, 2, 3, 4, 5, ect... ?
 Any good, or total crap?

We just have to rephrase it (slightly) to be proper math. :-P
For all n in IN: n + 0.5 is in the intervall (-oo, oo). [Where (-oo, oo) = IR.]
But of course, there is no k e IN such that n + 0,5 = k, for any n e IN.
So for all n e IN: n + 0.5 !e IN n IR [n + 0.5 !e IN n (-oo, oo)].
Hope this helps.
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On second thought... We might DEFINE
     IN + x := {n + x : n e IN}. (x e IR)
In this case we might indeed state:
     IN + 0.5 c IR.
But of course (in this case)
     IN + 0.5 n IN = {}.
It seems to me, that this is what you have/had in mind.