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Discrete versus Continuous


Date: 08/24/98 at 02:40:06
From: Andrew Jacobson
Subject: Discrete Math  

What is Discrete Math? How do you use it?


Date: 08/24/98 at 03:13:00
From: Doctor Pat
Subject: Re: Discrete Math  

Andrew,

Mathematical ideas are often divided into two types, those that are 
continuous, and those that are discrete. 

An example of continuous is the number line. Between any two points, 
there are always more points.  

For discrete sets, this is not true. For instance, in baseball there 
are four bases. If you get a hit it is either a one-base hit (what we 
call a single), a two-base hit, a three-base hit, or a home run.  
There is no such thing as a 2 1/2 base hit. 

Discrete things are found in bundles or lumps, and you can only have 
certain numbers of them. 

Money is another discrete idea because you can not sell anything for 
$0.005. Prices can be grouped for specials, like 2 for 99 cents, but 
if you buy one it is either 49 cents or 50 cents. Discrete does not 
mean it has to be whole numbers, but it does mean there are only some 
that can be chosen, and some can not.  

Discrete sets can be infinite, but they can not be infinitely 
divisible. For example, the counting numbers from 1 to infinity are 
discrete, because, like the bases in baseball, you go from one to two 
and then to three but not the points in between. The number line from 
0 to 1 is not discrete but continuous, because between any two points 
in the set, there is always another point. This is the key that makes 
the difference. In discrete we can talk about things that are "next to" 
each other, with nothing between them, while in continuous sets we 
cannot.  

This is sort of a complex idea, and I hope I have helped you understand 
a little about what it means.  

- Doctor Pat, The Math Forum
Check out our web site! http://mathforum.org/dr.math/   
    
Associated Topics:
High School Discrete Mathematics

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