## Lesson 1 - Numbers and Numerals

For this lesson I will assume you do not know the concept of numbers or numerals. First, what is a number? It is a quantity. Let's say you are thirsty and need some glasses of water. How much water do you need? At times you might need only a glass of water. At other times you might want a glass followed another glass. And yet at other times you might need a glass followed by another glass which is still followed by another glass.

If you only need a glass then you need

__one__glass of water. The quantity of glasses of water is one.

If you need a glass followed by another glass then you need

__two__glasses of water. The quantity of glasses of water is two.

If you need a glass followed by another glass which is followed by yet another glass then you need

__three__glasses of water. The quantity of glasses of water in this case is three.

In everyday usage we assign numerals to the quantities.

The number one is represented by the numeral 1.

The number two is represented by the numeral 2.

The number three is represented by the numeral 3.

**Adding and Counting**

Let's say we have one glass of water and we wish to make it two. In this case we add one glass of water to what is already there. If we add a glass of water then we denote it by + 1. The + tells us that we added and the numeral after it tells us how many we added. If we wish to have three glasses of water and we only have two then we add one glass of water to it. In this case we have 2 + 1 = 3. The 2 tells us how many we had before. The + tells us that we are adding. The 3 tells us that we now have three glasses of water. The = is the equals sign. It tells us that the quantities on both sides of the equals sign are the same in quantity.

2 + 1 = 3 could be read in everyday language as "two plus one equals three".

**Other numbers and numerals**

To start out counting in everyday usage, we first start with the number one (1). To continue counting we add one to it (+1) to get two (2). To get to the next counting number we add one to it again and get three (3). Thus far we have:

1 + 1 = 2

2 + 1 = 3

We can continue to get another quantity yet higher than three which is four written as a 4.

3 + 1 = 4

Then a quantity called five (5) follows.

4 + 1 = 5

Then six (6), seven (7), eight (8), nine (9), and then ten (10).

5 + 1 = 6

6 + 1 = 7

7 + 1 = 8

8 + 1 = 9

9 + 1 = 10

You might be curious as to why ten is represented by two numerals (namely 1 and 0) instead of a numeral of its own. In this case the 1 stands for the quantity ten. Think of the numbers we just covered as this:

1 is 01

2 is 02

3 is 03

4 is 04

5 is 05

6 is 06

7 is 07

8 is 08

9 is 09

10 is 10

Since we have exhausted the everyday numerals, we then write the 1 in the next column. We can continue counting if we so wish.

10 + 1 = 11

11 + 1 = 12

19 + 1 = 20

And so on. In the case of 12, the 2 is in the ones' place and the 1 is in the tens' place.

There is another quantity which we have not yet covered. This is the quantity of zero also written as (0). Zero is such a quantity that

0 + 1 = 1.

Zero plus one equals one. Now practice counting: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11...

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