What Type Of Numbers Do We Use To Count Nothing?

One of the most basic abilities we have as humans is our ability to count.  We can visualize and see various number of objects in our physical world and some how know how to make sense of what we are seeing.

For example when a child is very young they might say they are three years old by raising 3 fingers- each finger representing a year of age.

Counting numbers is one of the most basic math functions we do, so it’s important we understand the type of numbers we use to count.

We count “things” using the Natural Numbers.

Natural Numbers- positive integers greater than zero- i.e.  1, 2, 3, 4, ……

So, what if we are asked to look inside a garage and count how many cars we see?  Well if  see 1 or 2 cars we can answer the question using Natural Numbers.  However what if we don’t see any cars?  Did we count a zero car?  Yes in a way we did count zero cars however we don’t have a counting number to express that value.   Fortunately people thousands of years ago had that same problem, i.e. trying to express when they counted “nothing”.

So ancient mathematicians invented the symbol zero- 0.   Our number system took a big leap forward with the invention of zero and when we add zero to the Natural Numbers we get the powerful set of numbers called the Whole Numbers.  As time went on humans continued to invent more complex number systems that solved their problems.  So as your homeschooler is doing some pretty fancy math using Real and Complex Numbers remember that it all started from the basic need to count.