Prince George of Cambridge - Incorrect title

Don't you think it would be reight to adress him as:
George Aleksander Louis Mountbatten-Windsor, Prince of England, Duke of Cambridge.
Exactly like his father!!
If you look at: http://www.royal.gov.uk/ThecurrentRoyalFamily/TheRoyalFamilyname/Ov... Do it look like the English don't think there is anything but England, thus they just adress as prince and princess but I think the correct title most be of England, You can't just be a prince, you need to be prince of something!!

The members of the royalty go through a chain of title and style changes throughout their lives. in his birth registration, George was listed as H.R.H. Prince George Alexander Louis of Cambridge. His father was born H.R.H. Prince William of Wales because his father's highest title was Prince of Wales. William became Duke of Cambridge by Royal Decree upon his marriage. George, William and Charles were princes by birth. George's mother is a Duchess by marriage. While H.R.H. is an appropriate style for her, she would not be allowed Princes until her husband's investment as Prince of Wales. The British have there way of doing this. It's not like you Googled John Smith and got 992 million responses. Google Prince George of Cambridge and you only get 12 million responses but there all about the same boy.