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what does f mean with arrow on top of it?

Mathematics
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likely its a vector, but it could be other things
no it has to do with math proofs
is it like inverse function or what?

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Other answers:

with an arrow?? hmmm....usually an inverse has a -1 as its exponent...what kind of proofs (what subject/level of math) are you doing?
functions
injections, surjections etc
and there is an arrow to the left and arrow to the right above letter f
http://en.wikipedia.org/wiki/Bijection,_injection_and_surjection http://www.math.fsu.edu/~pkirby/mad2104/SlideShow/s4_2.pdf i dont know what the notation means, but the above links may be able to help
is it image of X or something?
i have no idea what the notation means. but those links should be able to help. heress some more http://www.cs.uwyo.edu/~jlc/courses/2300/hw/hw19d.pdf http://www.physicsforums.com/showthread.php?t=345400

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