But clearly, if we add up all the infinite fractions between 0 and 1, they would add up to 1.
0.9 and 0.8 are in that set, so they would add up to at least 1.7. In fact if you give me any positive number I can give you a (finite!) set of (distinct) fractions less than 1 which sum to more than that number. In other words, the sum is infinite.
I meant to say that we can infinitely divide the numbers between 0 and 1 and then match each with an integer. But I realized that the former wouldn’t be rational numbers, they would be real numbers.
That aside, I see now that the original idea behind the meme was mistaken.
0.9 and 0.8 are in that set, so they would add up to at least 1.7. In fact if you give me any positive number I can give you a (finite!) set of (distinct) fractions less than 1 which sum to more than that number. In other words, the sum is infinite.
I meant to say that we can infinitely divide the numbers between 0 and 1 and then match each with an integer. But I realized that the former wouldn’t be rational numbers, they would be real numbers.
That aside, I see now that the original idea behind the meme was mistaken.