### Home > INT2 > Chapter 12 > Lesson 12.1.3 > Problem 12-34

12-34.

What do you think 0! is equal to? Homework Help ✎

Try it on your calculator to see what you get.

What does

_{8}*P*_{8}mean? What*should*_{8}*P*_{8}be equal to? Write_{8}*P*_{8}using the factorial formula. Why is it necessary for 0! to equal 1?Do you remember how to show that 2

^{0}= 1? You can use a sequence of powers of two like this:= 2 ^{3},= 2 ^{2},= 2 ^{1}, so= 2 ^{0}. Since= 1 you also know that 2 ^{0}= 1.

You can construct a similar pattern for 0!, starting with= 4! and then = 3!. Continue the pattern and make an argument to justify that 0! = 1.

1

Refer to the Math Notes box for help.