elementary

Pluralelementaries

1. 1
   adjective

   Very simple; requiring little thought, skill, or explanation.

   The detective dismissed the puzzle as elementary.

   Once you see the trick, the card game's strategy seems elementary.

   Similarsimple, easy, straightforward, trivial, basic

   Oppositedifficult, complex, complicated

2. 2
   adjective

   Relating to elementary school, the first stage of formal schooling for children roughly five to eleven years old.

   The district hired forty new elementary teachers this fall.

   Elementary classrooms tend to be more colorful than high-school ones.

   Similarprimary

3. 3
   adjective

   Concerned with the first principles or most basic parts of a subject.

   The handbook explains the elementary principles of contract law.

   An elementary grasp of grammar is enough to start writing simple sentences in Spanish.

   Similarbasic, fundamental, rudimentary, essential

   Oppositeadvanced

   Note

   The founding sense, and the key to the whole word. Latin elementum meant both one of the four elements of antiquity and the fundamentals of a subject, and English kept both meanings. This one pairs naturally with principles, grasp, knowledge and rules. An elementary grasp is a basic one, not necessarily an easy one. The cosmic half of elementum survives in the archaic "sublunary" meaning.

4. 4
   adjective

   Forming a basic component of something larger or more complex, such as a structure or process.

   Chemists treat atoms as the elementary units from which molecules are assembled.

   Supply and demand are elementary forces in any market economy.

   Similarfundamental, basic

   Note

   Science's version of the word marks the level where analysis stops: an elementary unit or step is one that larger structures are built from. Jeremy Bernstein, writing in American Scientist in 2012, speaks of "the physics of elementary particles", the most familiar case. The specialized uses for particles, reaction steps, matrices and polynomials all branch from here. When a scientist says elementary, read "basic constituent", not "easy".

5. 5
   nouncolloquialcountable or uncountableabbreviationellipsis

   Ellipsis of elementary school.

   Kids in elementary usually have just one teacher for most subjects.

   I haven't seen her since elementary.

   Note

   Here the adjective stands in for the whole noun phrase, in places such as the US, Canada and the Philippines where elementary school is the usual term. It works uncountably after a preposition (back in elementary, since elementary) and countably in school names like Lakeside Elementary, where it is capitalized. It is informal, so formal writing keeps the word school.

6. 6
   adjective

   Of a subatomic particle, not composed of smaller constituents; serving as a basic building block of matter.

   Quarks and electrons are elementary, while protons are built from smaller pieces.

   The Standard Model catalogs every known elementary particle.

   Similarfundamental

   Oppositecomposite

   Note

   The best-known scientific use, almost always heard in the phrase elementary particle. It is not a synonym for subatomic. A proton is subatomic but built from smaller pieces, so it is not elementary, while an electron is both. Subatomic says how small a particle is; elementary says it has no smaller parts.

7. 7
   adjective

   Straightforward and using only basic techniques, without requiring substantial knowledge of a particular field.

   Her argument is elementary, relying on nothing beyond high-school algebra.

   The manual assumes only an elementary familiarity with programming.

   Similarbasic, simple, straightforward

   Oppositeadvanced

   Note

   Mathematicians use it to describe the tools of a proof, not its difficulty. An elementary argument draws only on basic techniques and assumes little specialized background, yet it may still be long and intricate. Calling a proof elementary is therefore a neutral description, not the dismissal carried by the "very simple" meaning.

8. 8
   adjective

   Of a chemical reaction or step: involving only a single reaction step and a single transition state.

   The decomposition is elementary, proceeding through a single transition state.

   Kineticists break the overall mechanism into a chain of elementary steps.

   Note

   Chemists use it for a single rung of a mechanism, as in elementary step or elementary reaction. An overall reaction is usually a chain of such steps. The distinction matters in kinetics: an elementary step's rate law can be written directly from its molecularity, whereas an overall reaction's rate law must be found by experiment. In this sense the word is said of reactions and steps.

9. 9
   adjective

   Of a proof or method in number theory: making no use of complex analysis.

   Selberg and Erdős stunned mathematicians with an elementary proof of the prime number theorem.

   For over a century, Dirichlet's theorem on primes in arithmetic progressions resisted elementary methods.

   Note

   Number theory drew a sharp boundary around the word: an elementary proof is one that avoids complex analysis, with its contour integrals and analytic continuation. As with the "basic techniques" meaning, it says nothing about difficulty. Outside the fixed phrase elementary number theory, this usage is now mostly historical. In current writing, expect the phrase rather than the free-standing label.

10. 10
    adjective

    Of a matrix: performing a single row or column operation on another matrix when the two are multiplied together.

    Row reduction can be recorded as multiplication by a sequence of elementary matrices.

    Each elementary matrix comes from applying one row operation to the identity matrix.

    Note

    Linear algebra's elementary matrices are the identity matrix altered by a single row or column operation. Multiplying another matrix by one carries out that operation, so row reduction can be written as a product of them. They are invertible, and together they generate the general linear group, which is why they are called elementary: everything else of that kind can be built from them.

11. 11
    adjective

    Of a symmetric polynomial: belonging to the basic family that arises from Vieta's formulas, which connect a polynomial's coefficients to its roots.

    The elementary symmetric polynomials in x and y are x + y and xy.

    Vieta's formulas write a polynomial's coefficients, up to sign, as elementary symmetric polynomials of its roots.

    Note

    To get these, multiply the variables together a fixed number at a time, in every possible way, and add the results. In x, y and z that gives x + y + z, then xy + xz + yz, then xyz. Every symmetric polynomial can be rewritten in terms of them, a strict mathematical case of the "building block" meaning. The word almost always comes in the full phrase elementary symmetric polynomial.

12. 12
    nouncountable

    A supernatural being associated with one of the classical elements of earth, air, fire, and water.

    The medium claimed an elementary had attached itself to the old house.

    Folklore collected in the book describes elementaries haunting wells and hearths.

    Similarelemental

    Note

    An occultist's noun, countable, with the plural elementaries. Rollo Ahmed's The Black Art (1936) pairs it with demon: "the demon (or elementary) of the South-West wind". H. P. Blavatsky imagines a person who "falls down lower than an elementary". Theosophical writers sometimes distinguished it from elemental, reserving elementary for the earthbound astral remnants of the dead, so check which one a source means.

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