Might be nitpicky but because it’s already been addressed and it’s something a lot of people don’t realize, Carbon dating is one of many radiometric dating method. It’s almost never used for fossils because it has a known limit of around 50,000 years, little more in ideal circumstanced. Past that it will yield false results because of background radiation drowning out the remaining Carbon14 radiation.
The important part of the multiple dating methods is that multiple are used. So a common objection for example is that there could be contamination. The problem is, in addition to careful precautions and testing the surrounding earth for such contamination, we look for multiple tests to agree. If you just test carbon14 and it says 9000 years you have a certain amount of confidence, but if carbon, uranium, AND radium all say 9000 years then the idea it was contaminated in just the right amounts but those exact isotopes to produce a consistent measurement is a little silly. Take that and extend it to multiple samples from multiple fossils and suddenly you can be extremely confident.
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