Summation Formula
Kisielewicz (1988) rewrote the logical definition of antichains into the following arithmetic formula for the Dedekind numbers:
where is the th bit of the number, what can be written using the floor function as
However, this formula is not helpful for computing the values of M(n) for large n due to the large number of terms in the summation.
Read more about this topic: Dedekind Number
Famous quotes containing the words summation and/or formula:
“He maintained that the case was lost or won by the time the final juror had been sworn in; his summation was set in his mind before the first witness was called. It was all in the orchestration, he claimed: in knowing how and where to pitch each and every particular argument; who to intimidate; who to trust, who to flatter and court; who to challenge; when to underplay and exactly when to let out all the stops.”
—Dorothy Uhnak (b. 1933)
“In the most desirable conditions, the child learns to manage anxiety by being exposed to just the right amounts of it, not much more and not much less. This optimal amount of anxiety varies with the child’s age and temperament. It may also vary with cultural values.... There is no mathematical formula for calculating exact amounts of optimal anxiety. This is why child rearing is an art and not a science.”
—Alicia F. Lieberman (20th century)