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Prove that if a person a has infinitely many descendants (children, their children, etc.), then a has an infinite sequence

a_0, a_1, \ldots

of descendants (i.e.,

a = a_0

and for all

n \geq 1, a_{n+1}

is always a child of

a_n

). It is assumed that no-one can have infinitely many children.
Variant 1. Prove that if

a

has infinitely many ancestors, then

a

has an infinite descending sequence of ancestors (i.e.,

a_0, a_1, \ldots

where

a = a_0

and

a_n

is always a child of

a_{n+1}

).
Variant 2. Prove that if someone has infinitely many ancestors, then all people cannot descend from

A(dam)

and

E(ve)

Problem Statement