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>>Erdős found that for any primitive set, including infinite ones, that sum — the “Erdős sum” — is always finite. No matter what a primitive set might look like
by scrubs 4y ago
>>Erdős found that for any primitive set, including infinite ones, that sum — the “Erdős sum” — is always finite. No matter what a primitive set might look like, its Erdős sum will always be less than or equal to some number. And so while that sum “looks, at least on the face of it, completely alien and vague,” Lichtman said, it’s in some ways “controlling some of the chaos of primitive sets,” making it the right measuring stick to use.
Finite? Surely there must be an operation done to each element of the set before summing to achieve a finite bound.
- yunwal 4y agoThe paragraph directly before the one you quoted explains the sum: > For every number n in the set, plug it into the expression 1/(n log n), then add up all the results. The size of the set {2, 3, 55}, for instance, becomes 1/(2 log 2) + 1/(3 log 3) + 1/(55 log 55).
- S4M 4y agoIt said that the quantity sum(1/(n log n) for n in A) is always finite when A is a primitive set. The "operation done to each element of the set" is n -> 1 / (n log n).
- Enginerrrd 4y ago> "For example, rather than counting how many numbers are in a set, they might do the following: For every number n in the set, plug it into the expression 1/(n log n), then add up all the results. The size of the set {2, 3, 55}, for instance, becomes 1/(2 log 2) + 1/(3 log 3) + 1/(55 log 55). Erdős found that for any primitive set, including infinite ones, that sum — the “Erdős sum” — is always finite." Read the paragraph just above it.
- alanh 4y agoUpvoting because this post shouldn't have a negative score simply for being confused. Treating it as a reasonable question.