Right, that was a math typo. It really oscillates between 9% and 91%.
For example, 909090 of the numbers below a million have even length, i.e. 91%. As you increase the bound toward ten million, this fraction decreases until it hits a minimum of 9%, and then starts increasing again until you reach a hundred million, and so on.
Well, the old solution to what is the limit of: +1, −1, +1, −1, etc. was: (index starts at one, pattern is (-1)^(n+1))
Consider the cases:
a) +1, odd index
b) −1, even index
Average them.
0.
If that was applied directly, it’d be: (9+91)/2% = 50%.
You could argue that it should be broken down differently, because there’s different proportions here though.
You could also declare the answer undefined, and say infinity is about growth, it doesn’t have a value, for x % 2 (or odd or even number as the case may be), and averages are ridiculous. (And once you have a breakdown of cases, and probability what more is there?)
That is one of the puzzle in that 0+0+0+0+0… converges and has a value but +1-1+1-1+1-1… which seems to be like (1-1)+(1-1)+(1-1)+(1-1)… diverges (and the series with and without the paranthesis are not equivalent)
The strram idea gives it a bit more wiggleroom. Getting 1,0,1,0,1.. fish seems equivalent to getting 1⁄2 fish a day but 1,1,1,1,1.. seems twice the fish of 1,0,1,0,1,0,1,0… So which with the other methods are “can’t say anthing” there is maybe hope to capture more cases with this kind of approach.
Too bad its not super formal and I can’t even pinpoint where the painpoints for formalization would be.
Right, that was a math typo. It really oscillates between 9% and 91%.
For example, 909090 of the numbers below a million have even length, i.e. 91%. As you increase the bound toward ten million, this fraction decreases until it hits a minimum of 9%, and then starts increasing again until you reach a hundred million, and so on.
Well, the old solution to what is the limit of: +1, −1, +1, −1, etc. was: (index starts at one, pattern is (-1)^(n+1))
Consider the cases:
a) +1, odd index
b) −1, even index
Average them.
0.
If that was applied directly, it’d be: (9+91)/2% = 50%.
You could argue that it should be broken down differently, because there’s different proportions here though.
You could also declare the answer undefined, and say infinity is about growth, it doesn’t have a value, for x % 2 (or odd or even number as the case may be), and averages are ridiculous. (And once you have a breakdown of cases, and probability what more is there?)
That is one of the puzzle in that 0+0+0+0+0… converges and has a value but +1-1+1-1+1-1… which seems to be like (1-1)+(1-1)+(1-1)+(1-1)… diverges (and the series with and without the paranthesis are not equivalent)
The strram idea gives it a bit more wiggleroom. Getting 1,0,1,0,1.. fish seems equivalent to getting 1⁄2 fish a day but 1,1,1,1,1.. seems twice the fish of 1,0,1,0,1,0,1,0… So which with the other methods are “can’t say anthing” there is maybe hope to capture more cases with this kind of approach.
Too bad its not super formal and I can’t even pinpoint where the painpoints for formalization would be.