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How does the number system you've been working with in Part A relate to the real number system you usually use? Through analyzing a small, finite system, you've gained some understanding of number systems in general. Using units digit arithmetic, you've created an independent number system which was relatively easy to manage.
You've considered only the units digit for any one answer and in so doing have limited the size of your number system to just 10 numbers -- 0 through 9. You've seen that the finite system has its own addition and multiplication tables, additive and multiplicative inverse and identity elements, and computational rules. You've seen that the finite system does not have unique inverse elements for multiplication, as does the system of real numbers. Furthermore, you've seen that the computational rules sometimes coincide with those of the real number system. Let's explore some of the similarities and differences between the two systems.
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