What is the relationship between addition and factorization?

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Discussion Overview

The discussion explores the relationship between addition and factorization, specifically seeking a term that describes the process of addition analogous to how factorization relates to multiplication. The scope includes conceptual exploration and terminology in number theory.

Discussion Character

  • Exploratory, Conceptual clarification

Main Points Raised

  • One participant suggests that there should be a term analogous to factorization for addition.
  • Another participant proposes several potential terms including "addendize," "summandize," and "decompose."
  • A different participant argues that "decompose" is synonymous with factorization, particularly in the context of matrix decomposition.
  • One participant identifies "partition" as the term they were seeking, referencing its definition in number theory.
  • Another participant concurs that "partition" is the most commonly used term for this concept.

Areas of Agreement / Disagreement

Participants generally agree on the term "partition" as a suitable descriptor for the process of addition, but there is some disagreement regarding the appropriateness of other proposed terms like "decompose."

Contextual Notes

There may be limitations in the definitions of terms like "decompose" and "partition," as their meanings can vary in different mathematical contexts.

gnome
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_____ is to addition as factorize is to multiplication.

Is there a word for this?
 
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addendize? summandize? mm, decompose?
 
No, i think decompose means the same as factorize, i.e. multiplication, as in matrix decomposition.

But I think I just found my answer further down the page in the the "number partition" thread. I guess the word I'm looking for is "partition."

Wikipedia agrees:
"In number theory, a partition of a positive integer n is a way of writing n as a sum of positive integers."
 
It seems that one can use either sum or summate. I looked in the dictionary.
 
Gnome, I agree that 'partition' is used -- it's just about the only term I've read for that.
 

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