Rational numbers

Hello Special Agent,

Your mission, which we cannot allow you to refuse, is a dangerous one. You are being assigned to escort a very special number 1 back to its home village. What makes this number so special is that it will become the leader of all Natural Numbers. You do remember that Natural Numbers start with 1 and increase from there, don’t you? Good. Now read carefully as your travels will take you through some very perilous areas.

First you must pass through the Region of Rationales. This area contains any number in arithmetic, that is, all whole numbers, fractions, and decimals as well as their negative images. It is a very crowded place. Be especially aware of the roving vinculums. A vinculum is a division line just looking for an unsuspecting number to ensnare as a numerator or denominator in its fraction. For example, in the rational number 2/3, the line between the numerator 2 and the denominator 3 is the vinculum. They especially like to divide the number 1 so as to make interesting fractions. Your best hope is to avoid them, but, if you can’t, you must sacrifice other numbers in place of the 1 which you protect.

After leaving the Land of Rationales, you will enter the Forest of Integers. Here you leave behind the roving vinculums with their fractions, but you will encounter a very aggressive positive and negative population. In the forest an ongoing dispute exists between the positive and negative integers as to who is better and who can travel where. Since the 1 which you are entrusted with is a Natural Number, it is naturally (pun intended) a positive number. Should you encounter a group of negative numbers, you must not allow them to gain control of your positive number as it can be used in an equation to alter the balance of power within the forest. Your allies in getting through the forest are the other positive numbers, but you cannot rely on zeros as they are neither positive nor negative and don’t take sides in the matter.

Once through the forest you will enter the Plain of Whole Numbers. Negative numbers from the Forest of Integers and Region of Rationales cannot enter the plain; it is only for positive numbers 0 and up. You should not encounter much delay in crossing the plain, except for the massive herds of 0’s that roam through it. The other numbers are constantly rounding up the 0’s for use in number lines and other applications on the plain as well as the Forest and Rational Region. As mentioned earlier, no negatives can be found on the plain.

You should reach the Village of Natural Numbers within a week’s travel time. The numbers will be expecting you and have planned a major parade for your arrival. Please take some time to rest and recover from what is expected to be a very trying journey. Anticipate receiving additional orders while in the village.

Good luck, agent. This paper will not self destruct in five seconds.