Large Numbers - Large Numbers in Some Noncomputable Sequences

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:

    “Any novel of importance has a purpose. If only the “purpose” be large enough, and not at outs with the passional inspiration.”
    —D.H. (David Herbert)

    “Green grow the rushes-O
    What is your one-O?”
    —Unknown. Carol of the Numbers (l. 2–3)