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Subscripts

Date: 09/30/2002 at 22:31:22
From: Kevin
Subject: Subscript vs. Superscipt

Dear Dr. Math,

I'm currently taking Algebra 1 and I was curious as to what subscript 
actually denotes. I am aware that superscript refers to exponents, but 
I wanted to know in what kind of situation would someone use 
subscript, and in what level of math you learn about it.
 
Thanks!


Date: 09/30/2002 at 23:37:35
From: Doctor Peterson
Subject: Re: Subscript vs. Superscipt

Hi, Kevin.

A subscript is just a letter or number written to the right of 
something and below it. There's no reason it has to have any meaning; 
the superscript used for an exponent is just the notation someone 
chose long ago to use for powers, and has no inherent significance 
apart from that arbitrary choice.

Subscripts are used in various ways, not as specifically as exponents. 
For example, if we have a sequence of numbers and want to use a 
variable to represent them, we often use a subscript to indicate the 
index in the sequence. That is, if the sequence is 1, 2, 3, 5, 8, ... 
then

    a  = 1, a  = 2, a  = 3, a  = 5, a  = 8
     1       2       3       4       5

This notation lets us talk about

    a
     n

meaning the nth term in the sequence, so we can write statements like

    a  =  a    +  a
     n     n-1     n-2

We also use subscripts just to label variables:

    v  = new velocity, v  = old velocity
     n                  o

You will see both of these usages later in algebra, or in physics.

I can't think of any reason to write something like

    2
     3

since subscripts do not denote an operation between two numbers. Ah! 
I take that back! We also use subscripts to indicate a base; often, 
to avoid confusion, we write out the name of the base, as in

    10110    = 22
         two     ten

Even here, it's not an operation, like exponentiation, but just a 
notation where the subscript is sort of an adjective, as in the other 
cases.

If you have any further questions, feel free to write back.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/ 
Associated Topics:
Middle School Number Sense/About Numbers

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