Question: What do you get in R if you sum 1 with successive fractions 1/2, 1/3, 1/4, and so on all the way up to 1/500000th? Well, let's take a look….
Here's some simple code that sets up the vector of fractions:
v <- 1:500000 for (i in 1:length(v)) { v[i] = 1/i } > v[1] [1] 1 > v[2] [1] 0.5 > v[3] [1] 0.3333333 > v[500000] [1] 2e-06
And now, let's explicitly sum all the elements in the vector:
suma <- 0.0 for (i in 1:length(v)) { suma = suma + v[i] } > suma [1] 13.69958
This seems fine. So, let's take a look at what happens if we add the numbers up in reverse:
sumz <- 0.0 for (i in length(v):1) { sumz = sumz + v[i] } > sumz [1] 13.69958
Great, the same answer; it's all good, move along, nothing to see here….
Um, yeah, actually; let's take a closer look:
> print(suma,digits=15) [1] 13.6995800423056 > print(sumz,digits=15) [1] 13.6995800423055
Err- Houston…?