the projection f:R->R' fulfill that f(x+y)=f(x)+f(y) f(xy)=f(x)f(y) where R and R' are two set fulfilling the axions of real number. 1) Prove f(0)=0'(0' is the zero unit in R') 2) Prove f(1)=1' 3) Prove that c) f(m) = m', which (m E Z, m' EZ' ") and thus, further more prove J : Z -> Z' is bijective and isotonic 4) Prove that f(m) = m'',; m, nEZ, n / 0, m', n' EZ', n' # 0', f(m) = m', f(n) = n' and thus further more prove that " f : Q Q' is bijective and isotonic. 5) Prove f : R - R' is bijective and isotonic