Is it possible to get pure Hydrogen and Oxygen from Water?
Yes, that is pure hydrogen and pure oxygen bubbles forming. However, the water contains dissovled oxygen, nitrogen and other gasses in small quantities. As bubbles form on the electrodes, the dissolved gasses may come out of solution and enter the bubbles as they form. Then the bubble you collect, is not pure. Close, perhaps 99.9999% pure, but not perfect.