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Product Notation


Date: 10/26/2000 at 09:55:40
From: Daniel Geraldes Uzueli
Subject: The Pi Symbol - Other Math Uses

Dear Sir, 

I would like to confirm with you whether "Pi" also means, in one 
equation, the following:

     Pi(Xi) [i = 1 to f] = the multiplication of the terms of X with i 
                           changing from 1 until f.
Is it correct?

Thank you for your attention, 
Daniel Uzueli


Date: 10/26/2000 at 10:35:49
From: Doctor TWE
Subject: Re: The Pi Symbol - Other Math Uses

Hi Daniel - thanks for writing to Dr. Math.

You are correct, this:

     

would be read as "the product of all x-sub-i's for i is equal to 1 
through f," and means to multiply all of the x terms beginning with 
the first and ending with the fth.

Pi is a letter in the Greek alphabet that is their equivalent of our 
letter P. In math and science, we frequently use Greek letters to 
represent variables, constants, functions, and the like. Note that 
when we use pi to represent the ratio of the circumference to the 
diameter of a circle (3.14159...) we use the lowercase letter pi; it 
usually has a curvy top and short legs:

     

To represent the product function, we use the uppercase pi, which 
generally has a straight top and longer legs:

     

The product pi notation was developed to correspond to the summation 
sigma notation (which uses an uppercase Greek letter sigma in a 
similar fashion:

     

I hope this helps. If you have any more questions, write back.

- Doctor TWE, The Math Forum
  http://mathforum.org/dr.math/   
    
Associated Topics:
High School Definitions
High School Functions

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