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the mathematical symbol of today is the product symbol written with a capital pi and in the same way as we have for the sum symbol we use an index below the letter pi so here k starts with the value 1 goes through all natural numbers until we docHub the value n in the end hence this symbol here is a short notation for a product with exactly n factors more precisely we start with a1 times a2 times a3 and so on until we docHub a n of course a1 a2 and so on could be any numbers the important thing is only that we have an index involved on the left hand side we call it k but of course any other name would do it as well now you can see the whole thing here as an explanation for the product symbol but the formal definition should be given by a recursive definition this means that we first have to explain what the empty product should be in other words what happens when we set n to zero then the explanation from above does not make any sense because there are no numbers involved indeed the only
