If cells reproduce every 7 years, why do tattoos remain permanent?

It is said that every cell in the human body dies off and reproduces approximately every seven years (which leads to a philosophical idea that we are not in fact the same person we were seven years ago). I have read that this measure is only approximate, and may be a little longer. That said, why do tattoos... show more It is said that every cell in the human body dies off and reproduces approximately every seven years (which leads to a philosophical idea that we are not in fact the same person we were seven years ago). I have read that this measure is only approximate, and may be a little longer.

That said, why do tattoos remain permanent for much longer than 7 years? If the cells holding the ink actually died and reproduced, they wouldn't reproduce in the color of the ink, so why don't tattoos fade away completely after 7 years or so?
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