Evenness

Whole numbers can be odd or even. Number theory takes this further by introducing the concept of the degree of evenness of a whole number.

Any whole number X can be uniquely decomposed into the product of a power of two and an odd number.

    X = 2n (2a + 1)

The number 'n' here is the degree of evenness of X.

If you take the binary representation of X, you will find that the degree of evenness is the number of trailing zeros.

The degree of evenness is useful for some proofs in number theory.

Note: the number zero has an infinite degree of evenness

E"ven*ness, n.

The state of being ven, level, or disturbed; smoothness; horizontal position; uniformity; impartiality; calmness; equanimity; appropriate place or level; as, evenness of surface, of a fluid at rest, of motion, of dealings, of temper, of condition.

It had need be something extraordinary, that must warrant an ordinary person to rise higher than his own evenness. Jer. Taylor.

 

© Webster 1913.