Proof it of it is false or give counterexample of it is true

Proof it of it is false or give counterexample of it is true ?

There exists a one-to-one function f: Z rightarrow R.

Solution

A function f from Z to R is called one-to-one (or 1-1) if whenever
f (Z) = f (R) then Z = R.  

No element of R is the image of more than one element in Z.
But,

N is the set of all natural numbers like:1,2,3,4,5,....... The set has starting number 1 and the consecutive numbers increments by 1 . It has no end.

Z is integers( positive or negatives including zero).{-n------------4,-3,-2,-1,0,1,2,3,4,----n }

and R , the set of all real numbers, containing all rational and irrational numbers. Q, N , Z are the subsets of the set R.

here have every image of Z in R so that it is true.