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I don't want to use the word elemental, nor axiomatic, as both terms are already defined and in popular use.

Anyway, the way I want to use the term is not to describe the part, or type of part itself, but the quality that the part possesses; 'Something with which cannot be broken down any further possesses the quality x', where x is the word I seek, in the same way an axiom has the quality of being axiomatic.

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  • essence/essential - "broken into its essential parts"
    – miltonaut
    Commented Jun 18, 2016 at 22:48
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    I'm not sure I understood your question but atomic is described as "of or forming a single irreducible unit or component in a larger system", and it's corresponding noun would be atomicity. Does that come close to what you were looking for?
    – Yay
    Commented Jun 18, 2016 at 22:54
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    @Yay Ah yes, Atomic, I do not know why that didn't come to mind. Thanks ^.^ Commented Jun 18, 2016 at 23:06
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    @Yay you know what, i'm gonna go with atomicity, you should include it add as an answer :) Commented Jun 18, 2016 at 23:30
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    Possible duplicate of What is the word for something that is non-divisible?
    – herisson
    Commented Jun 19, 2016 at 2:54

7 Answers 7

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I think that the word atomic, which is often otherwise used in a physical sense, should be used here.

atomic a·tom·ic /əˈtämik/ adjective

  • of or relating to an atom or atoms. "the atomic nucleus"

  • Chemistry (of a substance) consisting of uncombined atoms rather than molecules. "atomic hydrogen"

  • of or forming a single irreducible unit or component in a larger system.

Oxford Dictionaries

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    I see the definition, but "atomic" is not the word that comes to mind when I contemplate things that can't be broken down any further. The ancient Greeks coined the term atom, but we now know that atoms can be broken down into protons, neutrons, and electrons, and that protons and neutrons can be broken down further into quarks. We talk of "splitting the atom". Commented Sep 19, 2016 at 2:57
  • But if it works for the OP, that's what matters! Commented Sep 19, 2016 at 3:19
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    @RichardKayser That’s hardly the fault of the Greeks. Atomic literally means ‘uncuttable’ (i.e., ‘unable to be cut/split up into smaller pieces’) – we were just too quick to apply it to a tiny thing in physics, not knowing that the thing we were thus (mis)naming was in fact not atomic. To me, atomic is absolutely a word I’d think of when I contemplate things that can’t be broken down any further. Commented Apr 24, 2019 at 13:57
  • @JanusBahsJacquet Agreed. And when we find the new word sub-atomic, atomic there refers to the thing we thought was atomic, but actually wasn't.
    – TimR
    Commented Aug 29, 2023 at 11:58
  • @JanusBahsJacquet Agreed. And when we find the new word sub-atomic, atomic there refers to the thing we thought was atomic, but actually wasn't.
    – TimR
    Commented Aug 29, 2023 at 11:58
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I'd go for irreducible, "not reducible; incapable of being reduced or of being diminished or simplified further".

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While I agree that atomic may be the best fit, indecomposable works too.

M-W:

indecomposable adjective

: not capable of being separated into component parts or elements

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I try to get to the root of the problem. The root of any problem exists as the basis for all resulting and related things and issues.

The root of a word is the basis of its evolution and usage in our language.

Mathematically, a root is a component of an amount, part of a denominator, a multiplicand.

The root is elemental

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  • A prime number used to be a number that could not be broken down any further. Then the algebraists began to insist that 1 is not a prime.
    – Airymouse
    Commented Sep 18, 2016 at 22:29
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"Simplex" is another one that would work.

"Simplex" derives from the same root as "simple," but is used more exclusively in the technical sense of being irreducible in form. I think "simplicity" is the noun form of both. It can be used to mean, "Freedom from division into parts."

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indiscrete: not discrete : not separated into distinct parts

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    Your answer could be improved with additional supporting information. Please edit to add further details, such as citations or documentation, so that others can confirm that your answer is correct. You can find more information on how to write good answers in the help center.
    – Community Bot
    Commented Aug 29, 2023 at 11:41
  • Not really. You can have a discrete group, which would be divisible.
    – Chenmunka
    Commented Aug 29, 2023 at 17:17
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Ineffable:

that cannot be expressed or described in language. (OED)

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  • add a citation or dictionary ref to your answer if you please.
    – lbf
    Commented Mar 15, 2018 at 23:31
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    I think this doesn't really fit, since an atom for example cannot be broken down any further, but that doesn't make it ineffable.
    – Laurel
    Commented Mar 16, 2018 at 0:34

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