Re:A Bad Trip to Infinity
by Viliam1234 on Tuesday March 28, 2023 @03:04PM
(#35346196)
> You can... (define "next number") ...with rationals (so I understand, but I can't give a procedure).
1/1
1/2, 2/1
1/3, 2/2, 3/1
1/4, 2/3, 3/2, 4/1
1/5, 2/4, 3/3, 4/2, 5/1
...
The first rational number is 0. Next is 1/1, that is 1.
Next number to a positive rational number is its negative version, for example 1/1 is followed by -1/1.
Next number to a negative positive number can be found by taking its absolute value (i.e. the previous number), locating it in the pyramid, and choosing the next number... skipping those fractions which can be simplified. For example -1/1 is followed by 1/2.
So it goes like this: 0, 1/1, -1/1, 1/2, -1/2, 2/1, -2/1, 1/3, -1/3... now we skip 2/2 because that can be simplified to 1/1, and proceed with... 3/1, -3/1, 1/4, -1/4...
1/1
1/2, 2/1
1/3, 2/2, 3/1
1/4, 2/3, 3/2, 4/1
1/5, 2/4, 3/3, 4/2, 5/1
...
The first rational number is 0. Next is 1/1, that is 1.
Next number to a positive rational number is its negative version, for example 1/1 is followed by -1/1.
Next number to a negative positive number can be found by taking its absolute value (i.e. the previous number), locating it in the pyramid, and choosing the next number... skipping those fractions which can be simplified. For example -1/1 is followed by 1/2.
So it goes like this: 0, 1/1, -1/1, 1/2, -1/2, 2/1, -2/1, 1/3, -1/3... now we skip 2/2 because that can be simplified to 1/1, and proceed with... 3/1, -3/1, 1/4, -1/4...