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In the early days of radiocarbon analysis this limit was often around 20,000 radiocarbon years.
However, the reason for this is understood and the problem is restricted to only a few special cases, of which freshwater clams are the best-known example.
Some may have mistaken this to mean that the sample had been dated to 20,000 radiocarbon years.
The second characteristic of the measurement of radiocarbon is that it is easy to contaminate a sample which contains very little radiocarbon with enough radiocarbon from the research environment to give it an apparent radiocarbon age which is much less than its actual radiocarbon age.
The field of radiocarbon dating has become a technical one far removed from the naive simplicity which characterized its initial introduction by Libby in the late 1940's.
It is, therefore, not surprising that many misconceptions about what radiocarbon can or cannot do and what it has or has not shown are prevalent among creationists and evolutionists - lay people as well as scientists not directly involved in this field.