Warp wrote:
>> Map each real number to a positive integer. Now for each number, take 
>> the real number whose first digit differs from the first digit of the 
>> first real, whose second digit differs from the second digit of the 
>> second real, etc. You've just constructed a real which is, by 
>> construction, not on your list that maps all real numbers to integers.
> 
>   I think that the concept you are trying to explain could become clearer
> if you also prove why the amount of rational numbers between 0 and 1 is
> the *same* as the amount of integers. (In other words, each rational
> number can be uniquely mapped to an integer, and there are no rational
> numbers that can't be.)

	Yes. And to be formally correct, he has to deal with the fact that 
0.3459999999.... is also 0.346 and adjust a few minor details to account 
for it.

	

-- 
"Auntie Em: Hate Kansas. Hate You. Took Dog. -Dorothy."


                     /\  /\               /\  /
                    /  \/  \ u e e n     /  \/  a w a z
                        >>>>>>mue### [at] nawazorg<<<<<<
                                    anl

Post a reply to this message