Dear Louis,
That’s a great observation about numbers. Whether you start counting backwards or forwards, numbers never seem to end.
To find out more about these mysterious numbers, I took your question to my friend Kevin Fiedler. He’s an assistant professor of mathematics at Washington State University.
He reminded me that there are a lot of different rules mathematicians follow. For instance, if you think of a number, you could always add one to it.
Think of the highest number you can. Maybe you can even write it down on a piece of paper. Now, add one to it. Try it again and again. Perhaps the simplest answer to your question is you can always add one to a number.
Fiedler reminded me that some numbers are whole numbers, such as 1, 2, 3, 4 and 5. But there are also numbers like 1.33333…, and the 3’s go on without end. A lot of the time mathematicians and engineers will round these numbers.
On your piece of paper, you can also try adding a decimal, like .3, to your number.
The answer to your question might also depend on what set of numbers you are using in the first place. Fiedler told me about a kind of math called clock arithmetic that uses the set of numbers 1 through 12.
You might just think of those numbers 1 through 12 like the hours on a clock.
For instance, in normal arithmetic, 8 + 5 equals 13. But in clock arithmetic the math works out a bit differently. The answer to 8 + 5 is actually one.
Imagine you place your finger on the number eight of an analog clock, that is, a clock with hands and numbers 1 through 12. If you have a real clock, you can try this at home. Put your finger on the eight. Now count to one and put your finger on the nine.
On the second count, put your finger on the 10. On the third count, your finger goes to the 11. Perhaps, you are seeing a pattern. On the fourth count, your finger will be on the 12.
Finally, on the fifth count your finger will land on the one. In clock arithmetic, 8 + 5 equals one.
Of course, even in clock arithmetic, the numbers don’t really end. Once you reach the number 12, you can go back to one and start again.
If you’re curious about numbers, chances are you’ve also heard of infinity.
Infinity is a bit weird, Fiedler said. Infinity is something larger than any other number we know about, but we can’t put an exact value or counting number on it like we can with numbers such as 10, 100, or 1000. Perhaps as you continue on your learning journey, you’ll investigate more about infinity.
You know, this wide range of numbers allows mathematicians, scientists and engineers to work on all kinds of different problems in our world. Who knows, maybe one day you will use your math skills to help change the world, too.
Sincerely,
Dr. Universe