🚀 go-pugleaf

On Fri, 25 Apr 1997 20:41:15 GMT, porges@sunfire.camb.inmet.com (Don
Porges) wrote:

>
>In article <5jamlt$7ng@samba.rahul.net>, Ken Smith  <kensmith@rahul.net> wrote:
>>
>>Proof:
>>
>>Any rational number can be written in the form of N/D.  If each rational 
>>number can be mapped to a integer there is a countable number of them.  
>>For any rational number an integer can be written using the following 
>>procedure:
>>
>>Write down the value in the form N/D.  If one of the numbers has less 
>>digits than the other add leading zeros to that number to make the number 
>>of digits equal.
>>
>>Starting at the left end of the number write down the left most digit of 
>>N and then the left most digit of D.  Next write beside those digits the 
>>next digit of N and the next digit of D.  Continue this process of taking 
>>one digit from each number until all of the digits have been used.
>>
>>Example:
>>
>>           12/345  ...>   012/345   ....>  304152
>>
>>Each rational number can thus be mapped to an integer and hence the 
>>number of rationals must equal the number of integers.
>>
>True, but isn't this unnecessarily complicated?  Why not just map
>12/345 into 12345?  As long as each rational maps onto exactly one
>integer, your proof stands.  (Therefore you have to specify that
>all rationals are to be reduced as far as possible before applying 
>the transformation.)
Actually the mapping for 12/345 should be right to left 2,5,1,4,0,3
building 304152. A mapping to 12345 would not be suffice. It is not
unique. example: using the 12/345 map to 12345 method; 123/45
would also map to 12345. The correct way of mapping 123/45 would
be 014253.
bob