>>13210476before i go to sleep i will tell you how my list enumerates all real numbers since im sure you wont be able to figure it out on your own, it is easier if you draw on paper
>>13210490im considering you want a list for all the positive real numbers, though the list including negative reals is just a little more complicated
the first number of the list is
>...000.000...the last number on the list is
>...999.999...the first and the last numbers are the bases of the paralellogram that you get if you represent the list with the following pattern
...
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0. 1 2 3 4 5 6 7 8 9 (decimal point row)
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
0 1 2 3 4 5 6 7 8 9
...
as you can see, the first number is the entire base of the left side ending with the first digit of the last row (which is zero), the last number is the edge of the right side ending with the last digit of the last row (which is 9).
then what is the second number?
you can get the second number by going through the entire left edge and then ending with the second digit of the last row, in other words, the second number is ...000.000...0001.
the third number is ...000.000...0002, which is obtained by going from the entire left edge and then ending with the second digit of the last row (which is 2). and so forth, until the tenth number, which is ...000.000...0009.
so far, these 10 numbers can be enumerated with natural indices, the first number is represented by [1][1] (or 11) where the first bracket indicates the row ( [1] is the first row, the top one of the parallelogram that extends indefinitely from the top amd the bottom) and the second bracket indicates the digit of that row, or the column of that row, obviously the number of the second bracket can only go through 1 to 9. The tenth number is [1][9] (or 19)
