Pattern or Sequence?

Date: 10/02/2003 at 11:54:37
From: Lisa 
Subject: Patterns and Sequences

What is the difference between a pattern and a sequence?  The terms
appear to be interchangeable.

Date: 10/02/2003 at 13:09:45
From: Doctor Peterson
Subject: Re: Patterns and Sequences

Hi, Lisa.

"Pattern" is a vague word without any clear definition; it is used in 
teaching, to describe a general category of recognition skills. 

Patterns might exist in sequences; they can also be found in geometry 
(like patterns on wallpaper, in two or more dimensions) or in logic 
(patterns of reasoning), and so on. Not all patterns involve 
repetition, or even mathematics. 

The Merriam-Webster dictionary defines "pattern", among other things, as

  a discernible coherent system based on the intended
  interrelationship of component parts

(None of their definitions sounds very mathematical; this is the 
closest.)

"Sequence" is a specific, clearly defined word used in mathematics. A 
sequence can be considered to be a particular kind of pattern; but in 
fact a sequence need not have a pattern in any real sense! The 
mathematical definition of "sequence" in Merriam-Webster is

  a set of elements ordered so that they can be labeled with the
  positive integers

So all we can really say is that some patterns can be found in 
sequences; otherwise there is no connection between the words at all!

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

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/