Positive Integer is Sum of Consecutive Positive Integers iff not Power of 2/Mistake/Second Edition

Source Work

 * The Dictionary
 * $2$
 * $2$

Mistake

 * A positive integer is the sum of two or more consecutive integers it is not a power of $2$.

This should actually say:


 * A positive integer is the sum of two or more consecutive positive integers it is not a power of $2$.

It is understood that "positive integer" is taken in its strictly positive sense.

With the statement as it stands, all integers, whether positive or negative, are trivially the sum of a sequence of integers, for example:


 * $2 = \paren {-1} + 0 + 1 + 2$


 * $-4 = \paren {-4} + \paren {-3} + \paren {-2} + \paren {-1} + 0 + 1 + 2 + 3$

This mistake is in fact a partial correction to its statement in the $1986$ edition :


 * An integer is the sum of a sequence of consecutive integers it is not a power of $2$.