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We have heard tell that Loegolas took Gimli Gloin's son with him because of thier great friendship, greater than any that has been between Elf and Dwarf. If this is true, then it is stand indeed: that a Dwarf should be willing to leave Middle-earth for any love, or that the Eldar shoudl recieve him or that the Lords of the West should permit it. But it is said that Gimli went also out of desire to see again the beauty of Galadriel; and it may be that she, being mighty among the Eldar, obtained this grace for him. More cannot be said of this matter
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And Arwen gave up her immortality because she didn't want to live forever after Aragorn had died, not because she had to to marry him.
Most importantly, had Aragorn been allowed in the undying lands
he just would have died faster the undying lands do not give immortality to races, infact
mortals die faster in the undying lands. That is what lead to the destruction of the Numenoreans, they thought they would be immortal if they could go to the undying lands.