I saw this somewhere but I can't remember the reason behind it.
1/3 + 1/3 + 1/3 = 1
1/3 = 0.333333333... recurring
0.333333 + 0.333333 + 0.3333333 = 0.999999999...
The summation (Sigma sum indexed by i bounded from 0 to x) of 9 divided by 10 * 10^i.
If you compute that, you'll see that the limit goes to 1.
That's just one unneccessarily complex way to look at it.
This is one of the advantages of mathematics in my opinion : by defining some axioms and building everything upon it, it is possible to prove things without actually having to check whether it works : if the axioms remain the same throughout the proof, and the proof is valid, the experimental results will follow.