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### Defining Modulus

```Date: 12/10/2002 at 11:43:15
From: Jeremy Stone
Subject: The use of the term 'modulus'

I understand when this term is used to describe the congruent b-c
relation as mod (b,m) as I have Excel for years, but why when we
apply it to graphs does it translate as 'absoluted/directed value of'?
```

```
Date: 12/10/2002 at 13:38:11
From: Doctor Peterson
Subject: Re: The use of the term 'modulus'

Hi, Jeremy.

The word "modulus" is just a very vague term. I looked it up in
Merriam-Webster and found even more definitions than you mentioned:

1 a : the factor by which a logarithm of a number to one base is
multiplied to obtain the logarithm of the number to a new base
b : ABSOLUTE VALUE 2
c (1) : the number (as a positive integer) or other mathematical
entity (as a polynomial) in a congruence that divides the
difference of the two congruent members without leaving a
remainder -- compare RESIDUE b
(2) : the number of different numbers used in a system of
modular arithmetic
2 : a constant or coefficient that expresses usually numerically
the degree to which a body or substance possesses a particular
property (as elasticity)

It comes from a Latin word that just means "small measure" (the
diminutive form of "modus"). The three parts of definition 1 above
are the mathematical uses, which are just three kinds of size that
can be measured; definition 2 is the scientific use, which similarly
applies to several different fields.

There is no specific connection among these uses except that they are
all numbers that measure something.

It's also worth noting that "mod" is used with different meanings in
math and in computer programming, and that many people get the wrong
impression that the remainder is the modulus, when (as the definition
above implies) it is actually the divisor. According to Merriam-
Webster, the definition of "modulo" (which is the ablative of
"modulus" in Latin) is

with respect to a modulus of (19 and 54 are congruent modulo 7)

What is Modulus?
http://mathforum.org/library/drmath/view/54363.html

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

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