*mei- (2) Look up *mei- at Dictionary.com
Proto-Indo-European root meaning "small."

It forms all or part of: administer; administration; comminute; diminish; meiosis; Menshevik; menu; metier; mince; minestrone; minim; minimum; minister; ministration; ministry; minor; minuend; minuet; minus; minuscule; minute; minutia; Miocene; mis- (2); mite (n.2) "little bit;" mystery (n.2) "handicraft, trade, art;" nimiety.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit miyate "diminishes, declines;" Greek meion "less, smaller;" Latin minus, minor "smaller," minuere "to diminish, reduce, lessen;" Old English minsian "to diminish;" Russian men'she "less."
*mei- (1) Look up *mei- at Dictionary.com
Proto-Indo-European root meaning "to change, go, move," "with derivatives referring to the exchange of goods and services within a society as regulated by custom or law" [Watkins].

It forms all or part of: amiss; amoeba; azimuth; common; commune; communicate; communication; communism; commute; congee; demean; emigrate; emigration; excommunicate; excommunication; immune; immutable; incommunicado; mad; mean (adj.1) "low-quality;" mew (n.2) "cage;" mews; migrate; migration; mis- (1) "bad, wrong;" mistake; Mithras; molt; Mstislav; municipal; munificent; mutable; mutant; mutate; mutation; mutatis mutandis; mutual; permeable; permeate; permutation; permute; remunerate; remuneration; transmutation; transmute; zenith.

It is the hypothetical source of/evidence for its existence is provided by: Sanskrit methati "changes, alternates, joins, meets;" Avestan mitho "perverted, false;" Hittite mutai- "be changed into;" Latin mutare "to change," meare "to go, pass," migrare "to move from one place to another," mutuus "done in exchange;" Old Church Slavonic mite "alternately;" Czech mijim "to go by, pass by," Polish mijać "avoid;" Gothic maidjan "to change."