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Halx is correct.
Sharpness is relative, you can sharpen anything to an uberfine point. You can make a knife out of plastic, sharpen the hell out of it, and cut materials all day softer than it. When you are talking about metal vs human hair, it is pointless to use exotic metals.
Titanium is actually more elastic than most metals but is also very hard. It does a very good job at cutting things when sharpened right , but that is overkill. The sharpest knives out there are made out of a ceramic, something you wouldn't normally consider sharp.
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