4 Part 1: The World of Numbers
The Counting Numbers ...........................................................................................................
People have a tendency to think that our number system was always there and was always as it
is now. On some level, that’s true. The desire, and need, to count things dates to early history,
but how people count and what people do with numbers have changed over the years. The need
to count is so fundamental that the whole system is built on the numbers people use to count.
The counting numbers, also called the natural numbers, are the numbers 1, 2, 3, 4, and so on. The
counting numbers are an infinite set; that is, they go on forever.
You might notice that the counting numbers don’t include 0. There’s a simple reason for that.
If you don’t have anything, you don’t need to count it. Zero isn’t a counting number, but for
reasons you’ll see shortly, it’s one that is used a lot. The set of numbers 0, 1, 2, 3, 4, and so on is
called the whole numbers.DEFINITION
The counting numbers are the set of numbers {1, 2, 3, 4, ...}. They are the numbers we
use to count. The counting numbers are also called the natural numbers.
The whole numbers are the set of numbers {0, 1, 2, 3, 4, ...} They are formed by adding
a zero to the counting numbers.Numbers didn’t always look like they do now. At different times in history and in different places
in the world, there were different symbols used to represent numbers. If you think for a moment,
you can probably identify a way of writing numbers that is different from the one you use every
day. Roman numerals are an ancient system still used in some situations, often to indicate the
year. The year 2013 is MMXIII, and the year 1960 is MCMLX.
Roman numerals choose a symbol for certain important numbers. I is 1, V is 5, X stands for 10,
L for 50, C for 100, D for 500 and M for 1,000. Other numbers are built by combining and
repeating the symbols. The 2000 in 2013 is represented by the two Ms. Add to that an X for 10
and three Is and you have 2013. Position has some meaning. VI stands for 6 but IV stands for 4.
Putting the I before the V takes one away, but putting it after adds one. Roman numerals
obviously did some jobs well or you wouldn’t still see them, but you can probably imagine that
arithmetic could get very confusing.MATH IN THE PAST
Ever wonder why the Romans chose those letters to stand for their numbers? They
may not have started out as letters. One finger looks like an I. Hold up your hand to
show five fingers and the outline of your hand makes a V. Two of those, connected at
the points, look like an X and show ten.