Lesson plan
Iterated binary operation
In mathematics, an iterated binary operation is an extension of a binary operation on a set S to a function on finite sequences of elements of S through repeated application. Common examples include the extension of the addition operation to the summation operation, and the extension of the multiplication operation to the product operation. Other operations, e.g., the set-theoretic operations union and intersection, are also often iterated, but the iterations are not given separate names. In print, summation and product are represented by special symbols; but other iterated operators often are denoted by larger variants of the symbol for the ordinary binary operator. Thus, the iterations of the four operations mentioned above are denoted : \sum,\ \prod,\ \bigcup, and \bigcap , respectively. More generally, iteration of a binary function is generally denoted by a slash: iteration of f over the sequence (a_{1}, a_{2} \ldots, a_{n}) is denoted by f / (a_{1}, a_{2} \ldots, a_{n}) , following the notation for reduce in Bird–Meertens formalism. In general, there is more than one way to extend a binary operation to operate on finite sequences, depending on whether the operator is associative, and whether the operator has identity elements.
Article summary
In mathematics, an iterated binary operation is an extension of a binary operation on a set S to a function on finite sequences of elements of S through repeated application. Common examples include the extension of the addition operation to the summation operation, and the extension of the multiplication operation to the product operation. Other operations, e.g., the set-theoretic operations union and intersection, are also often iterated, but the iterations are not given separate names. In print, summation and product are represented by special symbols; but other iterated operators often are denoted by larger variants of the symbol for the ordinary binary operator. Thus, the iterations of the four operations mentioned above are denoted : \sum,\ \prod,\ \bigcup, and \bigcap , respectively. More generally, iteration of a binary function is generally denoted by a slash: iteration of f over the sequence (a_{1}, a_{2} \ldots, a_{n}) is denoted by f / (a_{1}, a_{2} \ldots, a_{n}) , following the notation for reduce in Bird–Meertens formalism. In general, there is more than one way to extend a binary operation to operate on finite sequences, depending on whether the operator is associative, and whether the operator has identity elements.
Key claims
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Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
Bibliography
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Key claims and bibliography are generated from the same tracked claims and sources as the article page.