Dual number

Imagine you have a magic number called "dual number" that can help you understand how things change. Let's call it "D." Now, when you add D to any regular number, it becomes a new number that tells you not only the original number, but also how it changes. For example, if you add D to the number 3, you get a new number called 3+D. This number not only tells you that you started with 3, but also that it changes by a little amount represented by D.

Here's an example: Let's say you're riding your bike at a steady speed of 10 miles per hour. You can use the dual number to see how much your distance changes over a short time period. If you ride for 30 minutes, you can add a little bit of time to the regular 30 minutes and get 30+D, which tells you not only the original time but also a small change in time. Similarly, if you multiply a regular number by D, you get a new number that represents the amount of change it undergoes in a different direction.

Overall, the dual number helps us understand how things change by representing changes as a very small "D" added to regular numbers.