Pizza, sliced:
(Relevant to, is a finite whole greater than any of its proper parts?)
BTW, Euclid, opening remarks:
Axioms.
i . Things which are equal to the same, or to equals, are equal to each other.
ii . If equals be added to equals the sums will be equal.
iii . If equals be taken from equals the remainders will be equal.
iv . If equals be added to unequals the sums will be unequal.
v . If equals be taken from unequals the remainders will be unequal.
vi . The doubles of equal magnitudes are equal.
vii . The halves of equal magnitudes are equal.
viii . Magnitudes that can be made to coincide are equal.
ix . The whole is greater than its part.
(This axiom is included in the following, which is a fuller statement:—)
ix’. The whole is equal to the sum of all its parts . . .
In context of course the wholes are finite (the Greeks rejected the actual infinite) and the parts, proper ones.
Food for thought from 2300+ Years ago. END