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 follo

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.

Answer 3

In simple terms, inclusive means within and the number n, while exclusive means within and without the number n.

Note: that each argument should be marked its "clusivity"/ "participation"

# 1 (inclusive) through 5 (inclusive)
1 <= x <= 5 == [1, 2, 3, 4, 5]

# 1 (inclusive) through 5 (exclusive)
1 <= x < 5 == [1, 2, 3, 4]

# 1 (exclusive) through 5 (inclusive)
1 < x <= 5 == [2, 3, 4, 5]

# 1 (exclusive) through 5 (exclusive)
1 < x < 5 == [2, 3, 4]