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I had a very nice Russian title and subtitle...
...but it occurred to me that they might make people think I wasn't a real human
Created on 2005-01-22 12:04:44 (#5854780), last updated 2009-11-22
620 comments received, 984 comments posted
Basic Account [Gift]
122 Journal Entries, 1 Tag, 0 Memories, 0 Virtual Gifts, 5 Userpics
Basic Info| Name: | Misha |
|---|---|
| Birthdate: | 1989-04-26 |
Bio| ... → Hn(X,A) | → Hn(X) | → Hn(A) | → Hn+1(X,A) | → Hn+1(X) | → Hn+1(A) → ... |
Theorem: Almost all natural numbers are very, very, very large.
Proof: It's intuitively clear that at least one very, very, very large number exists (otherwise, the term is meaningless): let one such number be L. Any number larger than L is certainly also very, very, very large. This is in fact "almost all" natural numbers: out of the infinite number of natural numbers, only finitely many (the ones {0,1,...L-1}) could possibly not be very, very, very large. QED
This would mean, in particular, that for any "small" number I could give you a billion very, very, very large numbers without ever repeating myself. But the difference between finite and infinite is a much wider gap than between one and a billion (or any other arbitrary number). If it somehow made sense (it doesn't) to pick a random natural number, there would be a probability of 1 that it will be very, very, very large.
Corollary: Any given natural number is relatively small.
Proof: Let N be any natural number. Define "very, very, very large" to mean "bigger than N". It follows that almost all natural numbers are bigger than N, making N rather insignificant in the large picture of things.
ConnectInterests (12):
arrow's impossibility theorem, bunny bunny toki toki, colorless green ideas, drawing on index cards, eating paper, foodtongue, hunting snarks, lemmas, made-up languages, mathcamp, rampant murderism, z80 assembly
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 | DarkerLine |  |
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