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the separating of any material or abstract entity into its constituent elements (opposed to ).
this process as a method of studying the nature of something or of determining its essential features and their relations:
the grammatical analysis of a sentence.
a presentation, usually in writing, of the results of this process:
The paper published an analysis of the political situation.
a philosophical method of exhibiting complex concepts or propositions as compounds or functions of more basic ones.
Mathematics.

an investigation based on the properties of numbers.
the discussion of a problem by algebra, as opposed to geometry.
the branch of mathematics consisting of calculus and its higher developments.
a system of calculation, as or .
a method of proving a proposition by assuming the result and working backward to something that is known to be true.
Compare (def 4).

Chemistry.

intentionally produced decomposition or separation of materials into their ingredients or elements, as to find their kind or quantity.
the ascertainment of the kind or amount of one or more of the constituents of materials, whether obtained in separate form or not.
Compare , .

.
Computers. .
noun (pl) -ses (-ˌsiːz)
the division of a physical or abstract whole into its constituent parts to examine or determine their relationship or value Compare synthesis (sense 1)
a statement of the results of this
short for psychoanalysis
(chem)

the decomposition of a substance into its elements, radicals, or other constituents in order to determine the kinds of constituents present (qualitative analysis) or the amount of each constituent (quantitative analysis)
the result obtained by such a determination

(linguistics) the use of word order together with word function to express syntactic relations in a language, as opposed to the use of inflections Compare synthesis (sense 4)
(maths) the branch of mathematics principally concerned with the properties of functions, largely arising out of calculus
(philosophy) (in the writings of Kant) the separation of a concept from another that contains it Compare synthesis (sense 6a)
in the last analysis, in the final analysis, in the ultimate analysis, after everything has been given due consideration
n.

1580s, “resolution of anything complex into simple elements” (opposite of synthesis), from Medieval Latin analysis (15c.), from Greek analysis “a breaking up, a loosening, releasing,” noun of action from analyein “unloose, release, set free; to loose a ship from its moorings,” in Aristotle, “to analyze,” from ana “up, throughout” (see ana-) + lysis “a loosening,” from lyein “to unfasten” (see lose). Psychological sense is from 1890. Phrase in the final (or last) analysis (1844), translates French en dernière analyse.

analysis a·nal·y·sis (ə-nāl’ĭ-sĭs)
n. pl. a·nal·y·ses (-sēz’)

The separation of a whole into its constituent parts for individual study.

The separation of a substance into its constituent elements to determine either their nature or proportions.

The stated findings of such a separation or determination.

Psychoanalysis.

analysis
(ə-nāl’ĭ-sĭs)

The separation of a substance into its constituent elements, usually by chemical means, for the study and identification of each component. ◇ Qualitative analysis determines what substances are present in a compound. ◇ Quantitative analysis determines how much of each substance is present in a compound.

A branch of mathematics concerned with limits and convergence and principally involving differential calculus, integral calculus, sequences, and series.