 |
 |
 |
|
 |
|
 |
|
 |
|
 |
|
 |
 |
|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
 |
|
|
Contents
Indices
|
Indices
Imagine you have a piece of paper.
You tear it into two. You then proceed to tear both pieces again into another
two. Now, you have 4 pieces of paper. If you tear it a third time, how many
pieces would you have? What about 6 times? What about fifteen times?
Based on what you already know,
tearing it a third time would give you:
2 x 2 x 2 = 8 pieces.
The sixth time would give you:
2 x 2 x 2 x 2 x 2 x 2 = 64 pieces.
Writing 2 x 2 x 2 x 2 ... endlessly
is not only time consuming, but also a waste of space as well as impractical. So
how can we shorten it?
This is where indices come in.
Simply, an index is written in the form:
ab
where a is the base and b
is the index. ab basically means:
ab = a x a x a
x a ... x a (b times)
Referring to the above example,
3rd time will give you 23 = 2 x 2 x 2 = 8 pieces,
6th time will give you 26 = 2 x 2 x 2 x 2 x 2 x 2 = 64 pieces,
and the 15th time will
give you 215 = 32768 pieces.
Indices are generally large
numbers. How large, you may say. Take a paper-tearing example. Assuming the
paper is 0.05 mm thick, if you tear it 20 times and stack all the pieces on top
of each other, the height of the paper is similar to the depth of a swimming
pool. And if you tear it 42 times and stack them all up, you can reach the moon.
 |
