Note:  this is a top-posted essay much more about floating-point
philosophy than about details.  Details follow from the philosophy,
and if philosophies don't match the desired details will never match
either.

>From that fundamental "take floats exactly at face value" view, what
.is_integer() should do for floats is utterly obvious: 

> Whether that's _useful_ to you depends on the application you're

writing at the time.

I think pretty much all the real world code that's been shown here for using .is_integer() is really about type errors (issues). The function at hand really wants integer inputs -- but wants to allow the user to be sloppy and provide a float type that happens to be an int. Given Python's duck-typing nature, maybe that's a good thing? I know I really discourage dynamic type checking....

Also, every example has been for small-ish integers -- exponents, factorials, etc -- not order 1e300 -- or inf or NaN, etc.

Finally, the use-cases where the value that happens-to-be-an-int is computed via floating point -- .is_integer() is probably the wrong check -- you probably want  isclose().

The other use-cases: and floor() and ceil() and round() all produce actual integers -- so no need for that anymore.