Function

It is clear that such examples might be multiplied indefinitely.

In fact, given any series X sub zero, X sub one, X sub two, X sub three, X sub N, and so on, which is endless, contains no repetitions, has a beginning, and has no terms that cannot be reached from the beginning in a finite number of steps, we have a set of terms verifying Peano's axioms.

This is easily seen, though the formal proof is somewhat long.

Let zero mean X sub zero, let number mean the whole set of terms, and let the successor of X sub N mean X sub N plus one.

Then, one, zero is a number.

That is, X sub zero is a member of the set.

Two, the successor of any number is a number.

That is, taking any term X sub N in the set, X sub N plus one is also in the set.

We have been whipped by the rebels, but it follows with arithmetical certainty that if we keep on fighting long enough, we will whip them in time.

Let X equal time and Y equal opportunity.

Then when X and Y come together, we shall have X plus Y, which will equal success.

Does my logic seem cogent to you, Mr.

Big Shoulders and Big Hands? Whitley stared at him in amazement and admiration.

I began teaching a district school when I was sixteen years old, and I would be teaching now if it were not for the war.

My specialty is mathematics.

X equals the war, Y equals me, and X plus Y equals me in the war.