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:
“Good gentlemen, look fresh and merrily.
Let not our looks put on our purposes,
But bear it as our Roman actors do,
With untired spirits and formal constancy.”
—William Shakespeare (1564–1616)
“Lord Byron is an exceedingly interesting person, and as such is it not to be regretted that he is a slave to the vilest and most vulgar prejudices, and as mad as the winds?
There have been many definitions of beauty in art. What is it? Beauty is what the untrained eyes consider abominable.”
—Edmond De Goncourt (1822–1896)