# 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 $0 / 0$, 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.