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A matematician, you are likely to agree, could not function without
a definition. Right?
...It provides a lesson on the unimportance of definitions. Students
often demand a definition of this or that, and they get really ticked
off if theydon't get one. But I suspect most real-world physicists get
along just fine without having a precise definition of "wave".
Biologists can't even agree on the definition of "plant" and "animal".