# Alteration vs Permutation - What's the difference?

alteration | permutation | Related terms |

## As nouns the difference between

is that

The act of altering or making different.
*
The state of being altered; a change made in the form or nature of a thing; changed condition.
*
(mathematics) A one-to-one mapping from a finite set to itself.
(mathematics, combinatorics) An ordering of a finite set of distinct elements.
(music) A transformation of a set's prime form, by applying one or more of certain operations, specifically, transposition, inversion, and retrograde.

## As nouns the difference between **alteration** and **permutation**

is that **alteration**is the act of altering or making different while

**permutation**is a one-to-one mapping from a finite set to itself.

# alteration

## English

### Noun

(*en noun*)

**1594**, ,

*Of the Laws of Ecclesiastical Polity*,

*…***alteration**, though it be from worse to better, hath in it inconveniences…

**1892**, ,

*…and I saw by the***alteration**in your face that a train of thought had been started.

*Webster 1913*)

### References

*# permutation

## English

### Noun

(*wikipedia permutation*) (

*en noun*)

*This***permutation**takes each element to the one following it, with the last mapped back to the first.

*There are six***permutations**of three elements, e.g. {abc, acb, bac, bca, cab, cba}.

### Anagrams

* importunate### See also

* (*combinatorics*) combination ----