I'm inspecting the Cantor Pairing function, that we can find on this link [here][1].

But the strange thing is that Mathematica is outputing a wrong result to me. The code below shows the strange behavior. When we plot the `Q2N1` function, the y axis does not corresponds to the correct value. See:

    Q2N0[q_] := (Numerator[q] + Denominator[q] + 1) (Numerator[q] + Denominator[q])/2 + Denominator[q]
    
    Q2N[q_] := Q2N0[Rationalize[q]]
    
    Q2N1[q_] := Q2N[N[q, 10]]
    
    Q2N1[0.2]
    
    Out[13]= 26
    
    Plot[Q2N1[x], {x, 0, 1}]

[![enter image description here][2]][2]


As we can see, confronting the code with the plot, when `x = 0.2` the correct value is `26`, but Mathematica plot function returns a value near of `2.25`. The truth is all returned values should be integers or very near to integers, so `2.25` could never be a result. Crazy.

Why this is happening? And, how can we have the correct output?


  [1]: https://en.wikipedia.org/wiki/Pairing_function#Cantor_pairing_function
  [2]: https://i.sstatic.net/gTF5R.png