When it's impossible to change or eliminate something, it's ineradicable. Unfortunately, your dad's ineradicable dislike of furry animals means you'll have to wait until you have a place of your own to get that dog you dream of.

The adjective ineradicable comes from eradicate, which means "totally destroy," and the prefix in-, "opposite of." So when something's ineradicable, whether it's a quality like hostility or a situation like inequality, there's just no way to destroy it. Though negative things are most often described as ineradicable, you can also praise your friend's ineradicable optimism or admire your teacher's ineradicable enthusiasm.

Definitions of ineradicable

adj not able to be destroyed or rooted out

ineradicable superstitions”
indelible, unerasable
not able to be removed or erased
inexpungeable, inexpungible
not capable of being expunged
inexterminable, inextirpable
incapable of extermination or extirpation
lasting, permanent
continuing or enduring without marked change in status or condition or place
able to be eradicated or rooted out
capable of being deleted
effaceable, erasable
capable of being effaced
exterminable, extirpable
capable of being totally destroyed or wiped out
obliterable, removable
able to be obliterated completely
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