(72 + 3)³ =

7- =14

= 4(7–3)

Further, you are able to evaluate the truth of well–formed legitimate expressions

20 + 4 =3³–3 (true)

71–8=7+10 + ½ (false)

4√16 =2 (2³) (true)

Now, consider the following expressions:

17 + 3√81 + 2 (5²) +6 = 3 (6²) -8

33 + 66+1 = 100

As the reader can easily determine (at least with a calculator) both of the expressions are well–formed, legitimate expressions in the language of arithmetic. Further, if the reader takes the time to compute them, it is easy to determine that they are both true—not only true, but each of them expresses the same fact, 100=100. Examine them carefully; and then consider the next expression:

8 + 27+1+64=100

Also states 100= 100 if we first change the sequence of this expression

1+8 + 27 + 64=100

then recode it into another form (chunking) leaving the meaning the same;

l³ + 2³ + 3³ + 4³=10²

This expression is also well formed, true and expresses the same fact as the last three. Note that

1+2+3+4=10

that is, the sum of the first four whole integers (on the left hand of the expression) adds up to the integer on the right. A response is immediate — I become curious as to whether I could add the next whole integer and still preserve the truth of the statement — that is: