Counting Numbers
I'll bring the flashlight. You bring the climbing gear!
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Numbers are the beginning and end of arithmetic. A powerful mode of representation, math is important in our lives, so it behooves us to learn the numbers.
As you know, there are many of them. Also there are different kinds of numbers. Here we look at the counting numbers, also called the natural numbers.
First, counting numbers are whole numbers, examples like 2, 7, 458, and 5619. No two are equal to each other. If A is a number and B is another number, A is not equal to B. Next, the numbers are ordered -- if A is a number and B is another number, then either A precedes B or B precedes A. Also, there is a first number in the ordering, namely the number 1.
Although there is a first number in the bunch, there is no last number! Every number has a next one. There is no number, A, that has no number after it in the order.
The ordering makes each successive number in the order greater in value by one than the immediately preceding number.
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When you examine counting, you realize that each number in the sequence adds one unit to the total count. You know the order to be expressed by the numbers:
1, 2, 3, 4, 5, 6, 7, ...
The numbers are also written as words:
one, two, three, four, five, six, seven, and so on.
As it happens, we start with one unit, called 1 (or one) -- it could also be called ^, or *, or whatever, but has long since been ruled 1. And we follow this with the commonly accepted:
2 = 1 + 1, or two equals one plus one.
Then we go to three, or::
3 = 2 + 1, or three is two plus one,
and so on, each number increasing the previous number by one unit. This is the basis of addition.
If we have two stacks of poker chips, we get the total number by counting those in the first stack and continuing the count in the second stack. The final count is the total and exactly equals the sum of the chips in the fist stack and the chips in the second stack. So if we know the number of chips in each stack, we can replace the counting with the simple addition of the number in each stack.
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There is no getting around the fact that you have to memorize the numbers to do even the most elementary calculations. To be skilled with numbers and avoid errors, you absolutely must commit them to memory. There are no shortcuts.
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