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
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| - Operasi biner teriterasi (in)
- Iterated binary operation (en)
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| - 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 (en)
- Dalam matematika, operasi biner berulang adalah sebuah perpanjangan dari sebuah operasi biner pada sebuah himpunan ke sebuah fungsi pada barisan terbatas dari anggota melalui penggunaan berulang. Contoh saat ini termasuk perpanjangan dari operasi penjumlahan hingga operasi notasi Sigma, dan perpanjangan dari operasi perkalian hingga operasi produk. Operasi lainnya, misalnya, teori-teori himpunan operasi gabungan dan irisan, juga sering diulang, tapi pengulangan tidak diberikan nama terpisah. Dalam cetakan, notasi Sigma dan produk diwakili oleh simbol yang spesial, namun operator berulang lainnya sering kali dilambangkan oleh variasi yang besar dari simbol untuk operator biner biasa. Demikian, pengulangan dari empat operasi disebutkan di atas dilambangkan (in)
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| - 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 and , respectively. More generally, iteration of a binary function is generally denoted by a slash: iteration of over the sequence is denoted by , 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. (en)
- Dalam matematika, operasi biner berulang adalah sebuah perpanjangan dari sebuah operasi biner pada sebuah himpunan ke sebuah fungsi pada barisan terbatas dari anggota melalui penggunaan berulang. Contoh saat ini termasuk perpanjangan dari operasi penjumlahan hingga operasi notasi Sigma, dan perpanjangan dari operasi perkalian hingga operasi produk. Operasi lainnya, misalnya, teori-teori himpunan operasi gabungan dan irisan, juga sering diulang, tapi pengulangan tidak diberikan nama terpisah. Dalam cetakan, notasi Sigma dan produk diwakili oleh simbol yang spesial, namun operator berulang lainnya sering kali dilambangkan oleh variasi yang besar dari simbol untuk operator biner biasa. Demikian, pengulangan dari empat operasi disebutkan di atas dilambangkan dan , masing-masing. Lebih umum, pengulangan dari sebuah fungsi biner secara umum dilambangkan oleh sebuah garis miringː pengulangan dari di barisan dilambangkan , berikut notasi untuk dalam . Secara umum, terdapat lebih daripada satu cara untuk memperpanjang sebuah operasi biner untuk mengoperasikan pada barisan terbatas, tergantung apakah operator asosiatif, dan apakah operator memiliki . (in)
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