~/tedtes/writing/math-foundations-for-reasoning-models

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Graphs and Computation

Parent

A parent is the node directly above another node in a rooted tree.

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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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