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Science Forum Index » Mathematics Forum » Title: Re: Shannon defeats Cantor = single infinity type
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| Author |
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| Daryl McCullough |
 Posted: Sat Dec 20, 2003 11:29 am |
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Guest
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|-|erc says...
Quote: "Daryl McCullough" <daryl@atc-nycorp.com> wrote
Look at the following two statements:
1. d is on the list
-> exists n, forall i,
digit number i of d = digit number i of number n
2. d can be approximated to any accuracy by numbers on the list
-> forall i, exists n,
forall j<i, digit number j of d = digit number j of number n
Same statement.
No, the first statement is false, but the second statement is true.
Quote: change forall j<i to forall j<=i for which the claim still holds
Statement 2 2nd part -
exists n, forall i,
forall j=i, digit j of d = digit j of n
No, you can't switch the quantifiers "forall i" and "exists n".
That's a logical error.
Quote: a formula is a type of algorithm
No, it's not. Here's a formula:
n is the largest prime number such that
n+2 is also a prime number
What algorithm is there to compute n?
--
Daryl McCullough
Ithaca, NY |
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