I'm trying the classic AirPassengers dataset in R and tried removing the seasonal component using `deSeas <- forecast::seasadj(decompose(d,"multiplicative"))`, but it doesn't seem to go away.  
Original data:  
[![enter image description here][1]][1]  
Seasonality viewed with `plot(decompose(d,"multiplicative"))`:  
[![enter image description here][2]][2]  
Seasonality adjusted with

    deSeas <- forecast::seasadj(decompose(d,"multiplicative"))
    plot(deSeas)

[![enter image description here][3]][3]  

But decompose still shows a seasonal pattern, `plot(decompose(deSeas,"multiplicative"))`:  

[![enter image description here][4]][4]  
  
I don't understand why there still is a seasonality. Should I de-seasonalize it again? Will arima be able to re-incorporate the single de-seasonalized or double de-seasonalized data back into the predictions that it tries to make?

  [1]: https://i.sstatic.net/A8b1e.png
  [2]: https://i.sstatic.net/fjMrN.png
  [3]: https://i.sstatic.net/Xj5Dd.png
  [4]: https://i.sstatic.net/4GhpR.png