R: is.integer and is.wholenumber

It is not the first time that a user is confused with this R output:

> is.integer(1)
[1] FALSE

The reason is the type of such a number is actually:

> typeof(1)
[1] "double"

The help of is.integer is actually doing a good job of pointing this out. However in this help an interesting suggestion is made for a function is.wholenumber. The purpose of this function is to check if the value of a number (opposed to the type) is an integer:

> is.wholenumber <-
+     function(x, tol = .Machine$double.eps^0.5)  abs(x - round(x)) < tol
> is.wholenumber(1)
[1] TRUE

Now the question is: why this tolerance of \(\sqrt{\epsilon}\)?

I probably would have implemented this function with the more naïve:

> my.is.wholenumber <- function(x) x==round(x)

i.e. use a tolerance of zero. May be a tolerance equal to the machine precision .Machine$double.eps could be useful (I am not sure of that), but a tolerance of \(\sqrt{\epsilon}\)?  I came up with this hypothesis. \(\epsilon\approx \)1.0e-16 so about 15 decimal places. The square root of this is about 7 decimal places. The default number of decimals in a print statement is 7:

> .Machine$double.eps
[1] 2.220446e-16
> .Options$digits
[1] 7

So may be the goal was to keep the print precision and the behavior of is.wholenumber in sync:

> 1.000005
[1] 1.000005
> 1.0000000005
[1] 1
> is.wholenumber(1.000005)
[1] FALSE
> is.wholenumber(1.0000000005)
[1] TRUE

It does not work perfectly:

> 1.00000005
[1] 1
> is.wholenumber(1.00000005)
[1] FALSE

Any better explanations around?