inequality

• inæquality (archaic, rare)

From Middle English inequalite, from Old French inequalité, from Medieval Latin inaequālitās, from Latin inaequālis (“unequal”), from in- (“not”) + aequālis (“equal”).

Morphologically inequal +‎ -ity and in- +‎ equality.

• (Received Pronunciation) enPR: ĭnĭkwŏl'ĭtē, IPA^(key): /ˌɪn.ɪˈkwɒl.ɪ.ti/

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• (US) enPR: ĭn-ĭʹkwŏ-lĭ-tē IPA^(key): /ˌɪn.ɪˈkwɑ.lɪ.ti/, [ˌɪn.ɪˈkwɑ.lɪ.ɾi]

inequality (countable and uncountable, plural inequalities)

1. An unfair, not equal, state.

   The inequality in living standards led to a civil war as the have nots rebelled.

   • 1976 February 14, A. Nolder Gay, “The View from the Closet”, in Gay Community News, volume 3, number 33, page 17:

     The traditional inequalities of marriage, such as changing her surname to his.

   • 2013 May 17, George Monbiot, “Money just makes the rich suffer”, in The Guardian Weekly‎^[1], volume 188, number 23, page 19:

     In order to grant the rich these pleasures, the social contract is reconfigured. […]   The public realm is privatised, the regulations restraining the ultra–wealthy and the companies they control are abandoned, and Edwardian levels of inequality are almost fetishised.

   • 2025 July 9, Oliver Wheeler, “Action stations...”, in RAIL, number 1039, page 68:

     With the growing awareness of climate change, congestion, and regional inequality, rail transport has re-emerged as a solution.

2. (mathematics) A statement that of two quantities one is specifically less than (or greater than) another. Symbol: ${\displaystyle <}$ or ${\displaystyle \leq }$ or ${\displaystyle >}$ or ${\displaystyle \geq }$ or ${\displaystyle \neq }$, as appropriate.

   The inequality ${\displaystyle x}$ is less than ${\displaystyle y}$, together with that ${\displaystyle y<z}$, allows us to deduce the inequality ${\displaystyle x<z}$.

   • 2015, Brandon Fogel, “Multideviations: The hidden structure of Bell's theorems”, in arXiv‎^[2]:

     I then specify a set of new tight Bell inequalities for arbitrary event spaces -- the "even/odd" inequalities -- which have a straightforward interpretation when expressed in terms of multideviations.

3. unevenness, irregularity
   • 1881, Charles Darwin, The Formation of Vegetable Mould Through the Action of Worms, page 313:

     When we behold a wide, turf-covered expanse, we should remember that its smoothness, upon which so much of its beauty depends, is mainly due to all the inequalities having been levelled by worms.

• (statement in mathematics): inequation

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• Thesaurus:inequality