The present participle of 'extinct,' meaning currently making something cease to exist or causing extinction.
Present participle form of 'extinct' (from Latin 'extinguere'). While grammatically possible, this form is rarely used in modern English—'extinguishing' is the standard modern form.
You almost never see 'extincting' in modern writing because 'extinguishing' became the standard, but if you're reading 18th-century natural philosophy texts, you might spot it discussing how hunting was extincting species!
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