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:
“they filled his belly
with large stones and sewed him up.
He was as heavy as a cemetery
and when he woke up and tried to run off
he fell over dead. Killed by his own weight.
Many a deception ends on such a note.”
—Anne Sexton (1928–1974)
“All ye poets of the age,
All ye witlings of the stage,
Learn your jingles to reform,
Crop your numbers to conform.
Let your little verses flow
Gently, sweetly, row by row;
Let the verse the subject fit,
Little subject, little wit.
Namby-Pamby is your guide,
Albion’s joy, Hibernia’s pride.”
—Henry Carey (1693?–1743)