What is the meaning of "exclusive" and "inclusive" when describing number ranges?

Question

Simple question but, I see exclusive and inclusive when referring to number ranges.

For example, this is a line from an algorithms book:

The following function prints the powers of 2 from 1 through n (inclusive).

What is meant by this? What makes a number range inclusive or exclusive?

Answer 1

In Computer Science, inclusive/exclusive doesn't apply to algorithms, but to a number range (more specifically, to the endpoint of the range):

1 through 10 (inclusive) 1 2 3 4 5 6 7 8 9 10  1 through 10 (exclusive) 1 2 3 4 5 6 7 8 9 

In mathematics, the 2 ranges above would be:

[1, 10] [1, 10) 

You can remember it easily:

• Inclusive - Including the last number
• Exclusive - Excluding the last number

Answer 2

The following function prints the powers of 2 from 1 through n (inclusive).

This means that the function will compute 2^i where i = 1, 2, ..., n, in other words, i can have values from 1 up to and including the value n. i.e n is Included in Inclusive

If, on the other hand, your book had said:

The following function prints the powers of 2 from 1 through n (exclusive).

This would mean that i = 1, 2, ..., n-1, i.e. i can take values up to n-1, but not including, n, which means i = n-1 is the highest value it could have.i.e n is excluded in exclusive.