OK let's settle this once and for all. During mitosis does the mother cell "die"/"stop existing" or does it continue existing in the daughter cells?

If you say it doesn't die than we literally are all still just that first cell that kept replicating and going through trillions of mutations, but there necessarily is an unbroken chain somewhere there to the first living being.

But the option that it "dies" just seems like nonsense, right?