If a knife is sharp it can be said to be "keen".

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Keen prices woo back cross-Border shoppers
Keen prices woo back cross-Border shoppers Cross-Border shoppers provided
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Note added at 2004-02-05 15:16:34 (GMT)
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The adjective \"keen\" has 6 senses in WordNet.

1. acute, discriminating, incisive, keen, knifelike, penetrating, penetrative, piercing, sharp -- (having or demonstrating ability to recognize or draw fine distinctions; \"an acute observer of politics and politicians\"; \"incisive comments\"; \"icy knifelike reasoning\"; \"as sharp and incisive as the stroke of a fang\"; \"penetrating insight\"; \"frequent penetrative observations\")
2. exquisite, keen -- (intense or sharp; \"suffered exquisite pain\"; \"felt exquisite pleasure\")
3. incisive, keen, sharp -- (very penetrating and clear and sharp in operation; \"an incisive mind\"; \"a keen intelligence\"; \"of sharp and active intellect\")
4. bang-up, bully, corking, cracking, dandy, great, groovy, keen, neat, nifty, not bad(predicate), peachy, slap-up, swell, smashing -- (very good; \"he did a bully job\"; \"a neat sports car\"; \"had a great time at the party\"; \"you look simply smashing\")
5. cutting, keen, knifelike, piercing, stabbing, lancinate, lancinating -- (as physically painful as if caused by a sharp instrument; \"a cutting wind\"; \"keen winds\"; \"knifelike cold\"; \"piercing knifelike pains\"; \"piercing cold\"; \"piercing criticism\"; \"a stabbing pain\"; \"lancinating pain\")
6. keen -- (having a sharp cutting edge or point; \"a keen blade\")