Formal Definitions
Formally, Sylvester's sequence can be defined by the formula
The product of an empty set is 1, so s0 = 2.
Alternatively, one may define the sequence by the recurrence
- with s0 = 2.
It is straightforward to show by induction that this is equivalent to the other definition.
Read more about this topic: Sylvester's Sequence
Famous quotes containing the words formal and/or definitions:
“That anger can be expressed through words and non-destructive activities; that promises are intended to be kept; that cleanliness and good eating habits are aspects of self-esteem; that compassion is an attribute to be prizedall these lessons are ones children can learn far more readily through the living example of their parents than they ever can through formal instruction.”
—Fred Rogers (20th century)
“What I do not like about our definitions of genius is that there is in them nothing of the day of judgment, nothing of resounding through eternity and nothing of the footsteps of the Almighty.”
—G.C. (Georg Christoph)