Date: Mar 1, 2013 5:11 AM
Author: Alan Smaill
Subject: Re: Matheology ? 222 Back to the roots
Nam Nguyen <namducnguyen@shaw.ca> writes:

> On 28/02/2013 7:51 PM, Virgil wrote:

>> In article <khUXs.345339$pV4.177097@newsfe21.iad>,

>> Nam Nguyen <namducnguyen@shaw.ca> wrote:

>>

>>> On 28/02/2013 8:27 AM, Frederick Williams wrote:

>>>> Nam Nguyen wrote:

>>>>>

>>>>> On 27/02/2013 10:12 PM, Virgil wrote:

>>>>>> In article <R8AXs.345282$pV4.85998@newsfe21.iad>,

>>>>

>>>>>> The set of all functions from |N = {0,1,2,3,...} to {0,1,2,...,9} with

>>>>>> each f interpreted as Sum _(i in |N) f(i)/10^1, defines such a

>>>>>> structure..

>>>>>

>>>>> That doesn't look like a structure to me. Could you put all what

>>>>> you've said above into a form using the notations of a structure?

>>>>

>>>> There is a set and a collection of functions on it. How does it fail to

>>>> be a structure?

>>>

>>> From what textbook did you learn that a structure is defined as

>>> "a set and a collection of functions on it"?

>>

>> Then give us your textbook definition of structure and show why the

>> above fails to meet it.

>

> Shoenfield, Section 2.5 "Structures". One reason the above fails is,

> you don't define, construct, the predicate (set) for the symbol '^'.

Who said that that is a predicate here?

> And that's just 1 reason amongst others. Do you admit it now that

> the above fails to meet the requirements of a language structure?

It fits with Shoenfield in the case where the only predicate

is equality.

--

Alan Smaill