Error

 

O Holy Night

O holy night! The stars are brightly shining,
It is the night of the dear Savior's birth.
Long lay the world in sin and error pining.
Till He appeared and the Spirit felt its worth.

There is still sin and error.

The mathematical statement 5±1 does not mean that there are only two answers: 4 and 6.  It means that any value between 4 and 6 is correct.  The term 5 in this example is the true answer, the mean/median/mode of a normal distribution, and the term 1 is the standard error.  Mathematically it could have also been expressed as 4 ≤ x ≤6, where x is the solution. 

The standard error is the square root of the variance.  A random number is a number with a non-zero variance, which means that it also has a non-zero standard error.  We can try to make that error as small as possible but “To err is Human”.  Scientists can design their experiments such that there is minimal error, but there will always be some error.  Engineers deal with the fact that there is variance and design systems such that the solution considers variance, error, randomness.

The solution of x²-1 as (x-1)*(x+1), x±1, should not be taken to mean that there are only two answers.  It should be taken to mean that any value of x between -1 and 1 is correct.  Otherwise you are effectively assuming that there is NO error. You might as well assume that there is no sin as well!