What common properties can be found in mathematical systems?
We previously defined multiplication modulo n. Now we are going to define addition modulo n. In this addition, the sum of two numbers is the remainder when the ordinary sum of the two numbers is divided by n. For example, in addition modulo 8, 6 +8 5 = 3 since 6 + 5 = 11 and the remainder when 11 is divided by 8 is 3 1. Find all sums modulo 8 of the numbers less than 8. What observation can you make? Include 0 in the set of numbers less than 8. 2. Similar types of addition can be defined for other numbers. Write a definition for addition modulo 5. Repeat #1 for sums modulo 5, sums modulo 6, and sums modulo 7. What observations can you make now? 3. An addition table can be made for each of the types of addition you just computed. Make an addition table for addition modulo 5, addition modulo 6, addition modulo 7 and addition modulo 8. Notice that with the definition of addition modulo n, we have another mathematical system. That is, a set of elements together with a rule for combining th
