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Definition of elimination : 1. Act of causing a quantity to disappear from an equation; especially, in the operation of deducing from several equations containing several unknown quantities a less number of equations containing a less number of unknown quantities.
2. the act of discharging or excreting waste products or foreign substances through the various emunctories.
3. The act of expelling or throwing off
4. The act of obtaining by separation, or as the result of eliminating; deduction. [ See Eliminate, 4.]

Synonyms:

euthanasia, dispersion, fratricide, excreting, genocide, keep, fall, purge, catharsis, displacement, defeat, culpable homicide, rout, riddance, settlement, voiding, extraction, demolition, drubbing, hammering, revenge, dumping, excretory product, avoidance, foul play, contract, clearance, excrement, body waste, emptying, beating, excreta, purgation, disposal, jettison, disqualification, butchery, hit, voidance, removable, reasoning by elimination

censorship, annihilation, expurgation, erasure

emission, extravasation, discharge, transudation, excretion, ejaculation, effusion, secretion, evacuation, exudation

blackballing, rejection, denial, eradication, disallowance, disapproval, repudiation, exclusion, ejection, expulsion, abandonment, blacklisting, curtailment

confinement, loneliness, aloneness, segregation, separation, misanthropy, captivity, isolation, standoffishness, aloofness, detachment, reclusion, solitude, apartheid, seclusion, xenophobia, anonymity, alienation, extirpation

disbarment, expatriation, amputation, prohibition, proscription, extradition, deportation, exile, removal, ban, excision, forbiddance, relegation, boycott, ostracism, renouncement, banishment, abscission, excommunication

extermination, butchering, massacre, manslaughter, dispatching, assassination, purging, liquidation, slaughter, slaying, snuffing, strangulation, execution, killing, hanging, asphyxiation, murder

disavowal, nullification, invalidation, dismissal, abnegation, negation, divorce, disclamation, deletion, cancellation, revocation, refutation, neutralization, withdrawal, abolition, destruction, dissolution, disaffirmation, obliteration, undoing, retraction, annulment, abolishment, extinguishment

Usage examples:

• And most of all he amused himself with figuring out the exact degree of his wife's astonishment and chagrin when, without consulting her, he achieved the triumph of Quarrier's elimination and the theatrical entry of Beverly Plank upon the stage. - "The Fighting Chance", Robert W. Chambers.
• By a process of elimination the authorities sifted the situation, and now it is whispered about that a decision has been reached, placing responsibility for the unique episode of a strike in the prison. - "Prison Memoirs of an Anarchist", Alexander Berkman.
• The process of elimination brought me to the absurd conclusion that the fault must lie in me. - "Greener Than You Think", Ward Moore.