Associated Topics || Dr. Math Home || Search Dr. Math

### 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

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search