Java is already installed in Linux Mint. You don't need to install it again.
If you are running Mint 7 then it has Sun Java 6 I don't think there is anything more up to date than that.
That is one of the reasons Mint is so good.
Fujitsu Lifebook AH532. Intel i5 processor, 6Gb ram, Intel HD3000 graphics, Intel Audio/wifi. Realtek RTL8111/8168B Ethernet.Lubuntu 13.10,Ubuntu12.10 (Unity), Mint16 (Cinnamon), Manjaro (Xfce).