Term grouping criteria
The term grouping criterion is a mathematical slang created by the mathematician Nicolás Atanes that says that if a series of infinite integer terms is written in no particular order, each term could be rearranged or decomposed to form a new series with the terms grouped "in order".
Uses[edit]
The criterion was first described following a published article on the series of the sum of infinite natural numbers and on the relation to the sum of infinite addends one[1].
When "in order" is mentioned, it means that there is a relationship between the terms, either finite or infinite, for example that all the terms are at a distance of one from the previous and next summand, or that each summand is the mean value between the two summands that surround it.
According to this criterion, suppose the following sum: . Since all the terms are integers, although in disorder, we can apply the criterion to write it "in order". If we add 2 to 3 and subtract two from 9, the terms will be at a distance of 1 from the nearest summand: .
In the most complex cases, Atanes showed that infinite chaos is impossible, and that the sum of a random distribution of numbers can be rearranged by distancing each number one unit from the nearest addend. You can start from a known sum (the sum of the infinite natural numbers) to modify it, but depending on the criteria, you can always rearrange them.
In popular culture[edit]
- The presenter of the Spanish television program Pablo Motos mentioned this topic in a program saying if "order in the abstract is important".
References[edit]
- ↑ Atanes, Nicolás (2022). "Casimir effect and sum of infinite natural numbers". Diario 16.
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