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The mathematical symbol of today is the product symbol written with a capital pi. We use an index, starting with 1 and going through all natural numbers until we reach n. This symbol is a short notation for a product with exactly n factors, starting with a1 times a2 and so on until reaching an. The important thing is that we have an index involved, named k. The formal definition of the symbol should be given by a recursive definition, explaining what the empty product should be when n is zero.
