Asked by Juddy
A student wants to know why, if we can define 0! as 1, we cannot define 1 over 0
Answers
Answered by
Steve
suppose 1/0 = x
That means that 1 = 0*x
But zero times anything is zero. There is no number x which can be defined as 1/0.
0! is useful because n! is a recursive definition.
That is,
n! = n * (n-1)!
3! = 3 * 2!
2! = 2 * 1!
1! = 1 * 0!
But, n! is also defined as the product of all the numbers from 1 to n. Since 1! is clearly 1, that means we must have 0! = 1.
That means that 1 = 0*x
But zero times anything is zero. There is no number x which can be defined as 1/0.
0! is useful because n! is a recursive definition.
That is,
n! = n * (n-1)!
3! = 3 * 2!
2! = 2 * 1!
1! = 1 * 0!
But, n! is also defined as the product of all the numbers from 1 to n. Since 1! is clearly 1, that means we must have 0! = 1.
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