Hasse Diagram/Examples/Genealogy from Terah to Joseph

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Example of Hasse Diagram

Recall the partial ordering on the set of people:

Let $P$ denote the set of all people who have ever lived.

Let $\DD$ denote the relation on $P$ defined as:

$a \mathrel \DD b$ if and only if $a$ is a descendant of or the same person as $b$.


Its dual $\DD^{-1}$ is defined as:

$a \mathrel {\DD^{-1} } b$ if and only if $a$ is an ancestor of or the same person as $b$.


Then $\DD$ and $\DD^{-1}$ are partial orderings on $P$.


Hasse-Diagram-Genealogy-Terah-Joseph.png

This Hasse diagram illustrates the restriction of $\DD$ to all $x$ of $P$ such that $x \mathrel \DD \text {Terah}$ and $\text {Joseph} \mathrel \DD x$, according to the Book of Genesis in the Bible.


Analysis

Genesis $11:26$:
And $\text {Terah}$ lived seventy years, and begat $\text {Abram}$, $\text {Nahor}$, and $\text {Haran}$.
Genesis $11:29$:
And $\text {Abram}$ and $\text {Nahor}$ took them wives: the name of $\text {Abram}$'s wife was $\text {Sarai}$; and the name of $\text {Nahor}$'s wife, $\text {Milcah}$, the daughter of $\text {Haran}$, the father of $\text {Milcah}$, and the father of Iscah.


Genesis $17:5$:
Neither shall thy name any more be called $\text {Abram}$, but thy name shall be $\text {Abraham}$; for a father of many nations have I made thee.
Genesis $17:15$:
And God said unto $\text {Abraham}$, As for $\text {Sarai}$ thy wife, thou shalt not call her name $\text {Sarai}$, but $\text {Sarah}$ shall her name be.


Genesis $20:2$-$3$:
And $\text {Abraham}$ said of $\text {Sarah}$ his wife, She is my sister: and Abimelech king of Gerar sent, and took $\text {Sarah}$.
But God came to Abimelech in a dream by night, and said to him, Behold, thou art but a dead man, for the woman which thou hast taken; for she is a man's wife.
Genesis $20:10$-$12$:
And Abimelech said unto $\text {Abraham}$, What sawest thou, that thou hast done this thing?
And $\text {Abraham}$ said, Because I thought, Surely the fear of God is not in this place; and they will slay me for my wife's sake.
And yet indeed she is my sister; she is the daughter of my father, but not the daughter of my mother; and she became my wife.


Genesis $20:20$-$23$:
And it came to pass after these things, that it was told $\text {Abraham}$, saying, Behold, $\text {Milcah}$, she hath also born children unto thy brother $\text {Nahor}$;
Huz his firstborn, and Buz his brother, and Kemuel the father of Aram,
And Chesed, and Hazo, and Pildash, and Jidlaph, and $\text {Bethuel}$.
And $\text {Bethuel}$ begat $\text {Rebekah}$: these eight $\text {Milcah}$ did bear to $\text {Nahor}$, $\text {Abraham}$'s brother.


Genesis $25:20$:
And $\text {Isaac}$ was forty years old when he took $\text {Rebekah}$ to wife, the daughter of $\text {Bethuel}$ the Syrian of Padanaram, the sister to $\text {Laban}$ the Syrian.


Genesis $25:24$-$26$:
And when her days to be delivered were fulfilled, behold, there were twins in her womb.
And the first came out red, all over like an hairy garment; and they called his name Esau.
And after that came his brother out, and his hand took hold on Esau's heel; and his name was called $\text {Jacob}$: and $\text {Isaac}$ was threescore years old when she bare them.


Genesis $29:10$:
And it came to pass, when $\text {Jacob}$ saw $\text {Rachel}$ the daughter of $\text {Laban}$ his mother's brother, and the sheep of $\text {Laban}$ his mother's brother, that $\text {Jacob}$ went near, and rolled the stone from the well's mouth, and watered the flock of $\text {Laban}$ his mother's brother.
Genesis $29:12$:
And $\text {Jacob}$ told $\text {Rachel}$ that he was her father's brother, and that he was $\text {Rebekah}$'s son: and she ran and told her father.
Genesis $29:28$:
And $\text {Jacob}$ did so, and fulfilled her week: and he gave him $\text {Rachel}$ his daughter to wife also.


Genesis $30:22$-$24$:
And God remembered $\text {Rachel}$, and God hearkened to her, and opened her womb.
And she conceived, and bare a son; and said, God hath taken away my reproach:
And she called his name $\text {Joseph}$; and said, The Lord shall add to me another son.

$\blacksquare$


Source of Name

This entry was named for Helmut Hasse.


Sources

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