Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: 2+2=4 ... How?
Replies: 9   Last Post: Sep 29, 2012 10:40 AM

 Messages: [ Previous | Next ]
 wilson Posts: 4 Registered: 9/27/12
Re: 2+2=4 ... How?
Posted: Sep 27, 2012 1:42 AM

On Thu, 27 Sep 2012 01:40:34 -0400, wilson <winslole@udayton.edu> wrote:

> On Thu, 27 Sep 2012 01:18:28 -0400, Brian M. Scott <b.scott@csuohio.edu>
> wrote:
>

>> On Wed, 26 Sep 2012 21:21:54 -0700 (PDT), Madhur
>>

>>> The natural numbers that we use are said to be derived
>>> from what so called Peano's Axioms.

>>
>> They *can* be; this is not the only possible formal
>> foundation for them.
>>

>>> While these axioms (listed below) give a method of
>>> building up counting numbers they do not define or
>>> construct basic arithmetic operations like addition,
>>> subtraction, multiplication, etc or basic comparisons
>>> like that of equality.

>>
>> Equality is assumed to be a known relation. The arithmetic
>> operations and the linear ordering on the natural numbers
>> are defined using the axioms. This is explained, albeit
>> briefly, in the Wikipedia article on the Peano axioms:
>>
>> <http://en.wikipedia.org/wiki/Peano_axioms?banner=none#Arithmetic>
>>
>> [...]
>>
>> Brian

>
> A bit more complicated:
>
> First you need another axiom. From the Wikipedia article:
>
> Addition is the function + : N × N ? N (written in the usual infix
> notation, mapping elements of N to other elements of N), defined
> recursively as:
>
> a + S(0) = a
> a + S(b) = S(a+b)
> Now can define 1 as S(0), 2 as SS()) and 4 as SSSS(0).
>
> the proof that 2 + 2 = 4 is then a matter of substituting the right
> thing in the right place.

sorry. my mistake. Define 2 as SS((0)).

Using Opera's revolutionary e-mail client: http://www.opera.com/mail/

Date Subject Author