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We all know that if you add any number of rational numbers you get a rational number. Yet the sum of an infinite number of rational numbers can be irrational (e
by dtf 13y ago
We all know that if you add any number of rational numbers you get a rational number. Yet the sum of an infinite number of rational numbers can be irrational (eg equation 2 in the article). Contradiction?
- acjohnson55 13y agoNot sure that's any less intuitive than getting a rational number from an infinite sum of integers, or a negative number from an infinite sum of positives. It is indeed a paradox until you rigorously define what you mean by "infinite sum", which is the whole point of the article :)