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Keeping track of family relations can be difficult.
If Edna marries your mother’s uncle Charlie, what should you call her?
Since each ancestor has two parents (one mother and one father), you have a total of 2n ancestors at level n: two parents, four grandparents, eight great-grandparents, sixteen great-great-grandparents, and so on.
Summing up, you have a total of 2 2 − 2 = 16 − 2 = 14.
For example, with n = 3 and m = 2, this says that your grandparents’ third-cousins are your third-cousins-twice-removed, and your third-cousins’ grandchildren are also your third-cousins-twice-removed.
Tracing back to n = 3 gives: In this diagram, your third-cousin (n = 3) shares two of your great-great-grandparents (level n 1 = 4 ancestors) but none of your great-grandparents (level n = 3 ancestors).
Your parents’ siblings are your aunts and uncles, and their children are your first-cousins (since you and they share the same grandparents, but not the same parents): If your cousins have children, then what are they to you?
If your father’s cousin’s daughter just had a baby boy, how should you two be introduced?
Who is your “great great aunt”, and how can you find your “first cousin twice removed”?
Finally, your sibling’s child is your niece (or nephew, if male), and their child is your great-niece (or great-nephew), and so on: (and similarly for “nephew” instead of “niece” at any level).
So now we know where your descendants’ cousins come from.
This attitude presumably has an evolutionary basis: our genes survived through the ages because our ancestors made efforts to help them survive by caring not only for themselves, but for their close relatives too.