The difference between the greatest five digit number and the greatest five digit number with all different digit is

1. Break Down the Problem

Let's identify the two numbers we need to work with:

1. The greatest five-digit number.
2. The greatest five-digit number with all different digits.

2. Relevant Concepts

• The greatest five-digit number can be found by placing the largest digits available in the highest place values.
• To find the greatest five-digit number with all different digits, we must use the digits 0-9 without repetition.

3. Analysis and Detail

1. Greatest five-digit number: This is simply $99999$.

2. Greatest five-digit number with all different digits: We can use the digits 9, 8, 7, 6, and 5:

   • The number can be constructed as $98765$.

4. Verify and Summarize

We now compute the difference between these two numbers: $99999 - 98765$

Performing the calculation: $99999 - 98765 = 1234$

Final Answer

The difference between the greatest five-digit number and the greatest five-digit number with all different digits is $1234$.