NaN versus NA in R

R has two different ways of representing missing data and understanding each is important for the user. NaN means “not a number” and it means there is a result, but it cannot be represented in the computer. The second, NA, explains that the data is just missing for unknown reasons. These appear at different times when working with R and each has different implications.

NaN is distinct from NA. NaN implies a result that cannot be calculated for whatever reason, or is not a floating point number. Some calculations that lead to NaN, other than [latex]0 / 0[/latex], are attempting to take a square root of a negative number, or perform calculations with infinities that lead to undefined results:

> sqrt(-1)
[1] NaN
Warning message:
In sqrt(-1) : NaNs produced
> Inf - Inf
[1] NaN

However, adding two infinities produces infinity:

> Inf + Inf
[1] Inf

NA is different from NaN in that NA is not a part of the IEEE standard for floating point numbers. NA is a construction of R used to represent a value that is not known, as a placeholder. NA says no result was available or the result is missing. It can be used in a matrix to fill in a value of a vector:

> c(1, 2, 3, 4, NA, 5, 6)
[1]  1  2  3  4 NA  5  6
> matrix(c(1, 2, NA, 4, NA, 6, NA, 8, 9), 3)
[,1] [,2] [,3]
[1,]    1    4   NA
[2,]    2   NA    8
[3,]   NA    6    9

Any operation with NA results in NA:

> 1 + NA
[1] NA
> sqrt(NA)
[1] NA
> NA + NaN
[1] NA

Update: David Smith at Microsoft covered NAs in a blog post today, too.

Image by Torindkflt / Wikimedia Commons.