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**