This question is inspired by Why is Arwen dying?
Aragorn is a half-elf, and if he chooses to move to the west together with all the elves, can he live on forever? Can Elrond make Aragorn immortal?
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Aragorn isn't a half-elf, he's a tiny fraction of an elf. Elros, who was a half-elf (actually 9/16), was his very remote ancestor.
But more importantly, the heirs of Elros were not given the choice to be elven or human, although the Valar did grant them unusually long life-spans. The heirs of Elrond were given that choice, which is why Arwen was able to choose a human life. There's a discussion thread here.
Can he live forever? Probably not:
Upon Sauron's defeat, Aragorn was crowned as King Elessar (translated as Elfstone in Quenya), a name given to him by Galadriel. (In Sindarin this becomes Edhelharn.) He became the twenty-sixth King of Arnor, thirty-fifth King of Gondor and the first High King of the Reunited Kingdom. His line was referred to as the House of Telcontar (Telcontar being Quenya for "Strider", the name he was known by in Bree). The Appendices of Return of the King explain that Aragorn married Arwen shortly afterwards, and ruled the Kingdom of Gondor and Arnor until the year 120 of the Fourth Age. His reign was marked by great harmony and prosperity within Gondor and Arnor, and by a renewal of communication and cooperation between Men, Elves, and Dwarves, fostered by his vigorous rebuilding campaign following the war. Aragorn led the forces of the Reunited Kingdom on military campaigns against some Easterlings and Haradrim, re-establishing rule over much territory that Gondor had lost in previous centuries. He died at the age of 210, after 122 years as king. It is said that the graves of Meriadoc and Peregrin (who had died in Gondor 58 years prior) were set beside his. He was succeeded on the throne by his son, Eldarion. Arwen, gravely saddened by the loss of her husband, gave up her mortal life shortly afterwards and was laid to rest in Lothlórien. Arwen and Aragorn also had at least two daughters. Upon hearing of Aragorn's death, Legolas built a grey ship in Ithilien, and sailed down Anduin and so to the Undying Lands; and with him, it is said, went Gimli the Dwarf. "And when that ship passed an end was come in Middle-earth of the Fellowship of the Ring."