Data frames and is.nan()

I was using sum(is.na(my.df)) to check whether my data frame contained any NAs, which worked as I expected, but sum(is.nan(my.df)) did not work as I expected.

> my.df <- data.frame(a=c(1, 2, 3), b=c(5, NA, NaN))
> my.df
  a   b
1 1   5
2 2  NA
3 3 NaN
> is.na(my.df)
         a     b
[1,] FALSE FALSE
[2,] FALSE  TRUE
[3,] FALSE  TRUE
> is.nan(my.df)
    a     b 
FALSE FALSE 
> sum(is.na(my.df))
[1] 2
> sum(is.nan(my.df))
[1] 0

Oh dear. Is there a reason for the inconsistency in behaviour? Is it for a lack of implementation, or is it intentional? What does the return value of is.nan(my.df) signify? Is there a good reason not to use is.nan() on a whole data frame?

In the documentation for is.na( ) and is.nan( ), the argument types seem the same (although they don't specifically list data frames):

is.na(): x R object to be tested: the default methods handle atomic vectors, lists and pairlists. is.nan(): x R object to be tested: the default methods handle atomic vectors, lists and pairlists.