Large Numbers in Some Noncomputable Sequences
The busy beaver function Σ is an example of a function which grows faster than any computable function. Its value for even relatively small input is huge. The values of Σ(n) for n = 1, 2, 3, 4 are 1, 4, 6, 13 (sequence A028444 in OEIS). Σ(5) is not known but is definitely ≥ 4098. Σ(6) is at least 3.5×1018267.
Some of the work by Harvey Friedman also involve sequences that grow faster than any computable function.
Read more about this topic: Large Numbers
Famous quotes containing the words large and/or numbers:
“Guilt plays a large part in my life.”
—Christine Zajac, U.S. fifth-grade teacher. As quoted in Among Schoolchildren, “September” section, part 3, by Tracy Kidder (1989)
“Think of the earth as a living organism that is being attacked by billions of bacteria whose numbers double every forty years. Either the host dies, or the virus dies, or both die.”
—Gore Vidal (b. 1925)