In Example 2.52 why did we stop at 26 and not at 28?
Suppose that we start with the universe that comprises only the 13 integers 2, 4, 6, 8,..., 24, 26. Then we can establish the statement:
For all n (meaning n = 2, 4, 6, ... , 26),
we can write n as the sum of at most three perfect squares.
The results in Table 2.24 provide a case-by-case verification showing the given (quantified) statement to be true. (We might call this statement a theorem.)

2 1+1 10 9+1 12 44 +4 14 9+4+1 16 16 18 1611 2016+ 4 22 99+4 24 16+4+4 26 25 1 6 41+1 8 4+4