The Laconic says it all.
This is a popular trope, both in real life and fiction.
Compare
Show Of Theseus, which is this trope applied to specific shows which have had parts replaced.
[[folder: Literature]]
- Early example is the Tin Woodman from The Wizard Of Oz. He pissed off a witch who enchanted his ax so that it would cut of pieces of him, and he went to a tinsmith to replace the missing parts. Eventually he was made entirely out of tin - but since it was a gradual process, he's still human Nick Chopper and not a new person.
- Brought up several times in The Fifth Elephant, generally in regards to a Dwarfish axe which has been passed down through the family for generations: sometimes the head needed replacing, other times the shaft, still more times the eye or the bit, but it's still the same ancestral axe.
[[folder: Live Action TV]]
- A popular example comes from the British sit-com Only Fools And Horses, where Trigger, one of the characters, is given a medal for owning the same broom for 20 years, although it has had 17 new heads and 14 new handles. When asked how can it be the same broom, Trigger produces a picture of himself and his broom and asks, "What more proof do you need?"
- Discussed in an episode of Star Trek Deep Space Nine. A former freedom fighter friend of Kira's gets injured and has part of his brain replaced with cybernetics. As more of his brain fails and is replaced, the less he's him. Eventually he's mostly cybernetics, and rather than continue the process Kira allows him to die.
[[folder: Real Life]]
- The USS Constitution, sometimes known as 'Old Ironsides' and the oldest commissioned warship still afloat. It has been around so long and had so many parts replaced that it's open to discussion if a single one is original.