Etymology
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Words related to independent

in- (1)
Origin and meaning of in-
word-forming element meaning "not, opposite of, without" (also im-, il-, ir- by assimilation of -n- with following consonant, a tendency which began in later Latin), from Latin in- "not," cognate with Greek an-, Old English un-, all from PIE root *ne- "not."

In Old French and Middle English often en-, but most of these forms have not survived in Modern English, and the few that do (enemy, for instance) no longer are felt as negative. The rule of thumb in English has been to use in- with obviously Latin elements, un- with native or nativized ones.
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dependent (adj.)

also dependant, late 14c., "relying for existence on;" early 15c. as "contingent, related to some condition;" from Old French dependant, present-participle adjective from dependre "to hang down," from Latin dependere "to hang from, hang down; be dependent on, be derived," from de "from, down" (see de-) + pendere "to hang, cause to hang; weigh" (from PIE root *(s)pen- "to draw, stretch, spin").

For spelling, see dependant (n.). In some cases the English word is directly from Latin dependentem (nominative dependens), present participle of dependere. From early 15c. in the literal sense of "hanging down, pendent." From 1640s as "subordinate, under the control of or needing aid from an extraneous source." Dependent variable in mathematics is recorded from 1852.

independence (n.)
1630s, "fact of not depending on others or another, self-support and self-government;" see independent + -ence. Earlier in same sense was independency (1610s). U.S. Independence Day (July 4, commemorating events of 1776) is recorded under that name by 1791.

An Old English word for it was selfdom, with self + dom "law," but in form this is closer to privilege (n.). The two concepts are not always distinguishable.
indie (n.)
"independent record company," 1945, shortening of independent. Among the earliest mentioned were Continental, Majestic, and Signature. Used of film production companies since 1920s, of theaters from 1942; extended by 1984 to a type of pop music issued by such labels.