Let's start from scratch:

HOW TO USE THIS PAGE!

This is what it looks like when we use indices:

What does this mean?

Indices describe repeated multiplication.

• 3 is the base. All the factors are 3.
• 4 is the index. It tells us how many factors there are.

This is the definition of indices. We will call it definiton 1.

Can we have more than one definition?

Here is a different definition (definition 2).

This says to start with 1. Then you multiply 1 by the base (3) as many times as the index says (4).

Why do we start with 1?

We will find both definitions useful.

These definitions are prototype definitions.

• We used 3 for the base, but the base can be any number.
• We used 4 for the index. This must be a counting number or postive integer. (We will remove this restriction in the next section).

What is a prototype?

Sometimes we need formal definitions. These are very precise statements which usually involve algebra so as to be general. Often its good to leave formal definitions until later, when you will have a better idea of what they are on about. So its up to you. Check them out now or leave them until later..

Formal definitions