...and yes, he died, the body died, and it was (as is said explicitly in UT)
"real and not feigned, but subject to the fears and pains and weariness of
earth, able to hunger and thirst and be slain, though because of their noble
spirits they did not die, and aged only by the cares and labours of many long
years." They were also never YOUNG in those bodies, and it required the
intervention of Iluvatar to make them in the first place, because they were not
like the Elvish hroar (a "replacement" for a body which had been severed the
from fea, the spirit), nor were they fanar, the "veils" used by the Ainur to
give themselves incarnate form. Gandalf even says it explicitly at one
point: "I have not passed through fire and death to bandy crooked
words..." There would be no reason for him to say DEATH unless he had
died and was aware of it. His Maia spirit lived and ultimately went "out
of thought and time" (which Tolkien said means he left the "circles of the
world" and apparently went to Eru, who sent him back again), but that body
died, and was replaced.
Having doubtless repeated what everyone else already said, I'll shut up
now.
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We need the faith to go a path untrod,
The power to be alone and vote with God.
--Edwin Markham