~/writing/math-foundations-for-reasoning-models $ ls
Graphs and Computation
Parent
A parent is the node directly above another node in a rooted tree.
~/writing/math-foundations-for-reasoning-models $ cat topic.md
Parent
Definition
A parent is the node directly above another node in a rooted tree.
Example:
A
/ \
B C
A is the parent of B.
A is also the parent of C.
Parent = direct predecessor in a rooted tree.
Parent Depends On Root
Parent relationships depend on how the tree is rooted.
Example:
A -- B -- C
If A is the root:
A
`-- B
`-- C
Then B is the parent of C.
If C is the root:
C
`-- B
`-- A
Then B is the parent of A.
Parent is a role created by the rooted structure.
Direct Relationship
Parent means directly connected one level above.
Example:
A
`-- B
`-- C
A is the parent of B.
B is the parent of C.
A is not the parent of C.
A is an ancestor of C.
Parent means one step above, not any earlier node.
Parent And Dependency
In some structures, a parent can represent what something comes from or depends on.
Example:
Expression
`-- Addition
|-- x
`-- 1
Addition is the parent of x and 1.
This means the two pieces belong directly inside that larger expression.
Parent relationships organize parts inside a hierarchy.
Final Summary
- A parent is directly above another node in a rooted tree.
- Parent relationships depend on the chosen root.
- Parent means one level above, not any earlier node.
- A node above another by multiple levels is an ancestor.
- Parent relationships help organize hierarchy.
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Continue the series.
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