I'm stuck on a problem, because I don't really understand what mapping is so I don't know what I can and can't do:
The problem is this:
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Suppose that f:R -> R is a map such that for all x,y in R (the real numbers)
f(x+y) = f(x) + f(y) and f(xy) = f(x)f(y)
Prove that f is either:
1) the identity mapping for all x in R. i.e. f(x)=x,
or
2) the zero mapping for all x in R. i.e. f(x)=0
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he gave us one hint, that somewhere in our proof that the fact that every positive real number is a square will be very useful.
I have no idea what to do and any help would be wonderful!
Thanks in advance!
2007-09-18
23:02:50
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2 answers
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asked by
greeneggs4spam
3
in
Mathematics