Assume your ancestor is correct when, on 5 January 1850, he says he is 50 years old. What does that mean?
He could have just turned 50 that very day, meaning he was born 5 January 1800. That would be the very youngest he could be on 5 January 1800---50 years and no days.
He could turn 51 the very next day, meaning he was born 6 January 1799. That would be the very oldest he could be on 5 January 1800 and still be 50, one day shy of his 51st birthday.
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