5+8=1∈Z12 because 5+8=13 and 13 divided by 12 leaves a remainder of 1 . multiplication) is often called "clock arithmetic". as a clock. The gray slider picks out n and the blue and red sliders pick out a and b to form their sum.

Yes, you are correct. In modular arithmetic, also known as clock arithmetic, we perform addition and multiplication operations within a fixed modulus. In this case, the modulus is 12.

When we add 5 and 8 in modulo 12 arithmetic, we get:

5 + 8 = 13

However, in modulo 12 arithmetic, we divide the result by 12 and take the remainder:

13 mod 12 = 1

Therefore, 5 + 8 is congruent to 1 modulo 12 (5 + 8 ≡ 1 (mod 12)).

In clock arithmetic, we can visualize the concept by imagining a clock with 12 hours. Adding 5 hours to the current time of 8 hours will give us 1 hour, as we "wrap around" the clock.

The sliders you mentioned can be used to experiment with different values of n, a, and b to observe the results of addition and multiplication in modulo n arithmetic.

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5+8=1∈Z12​ because 5+8=13 and 13 divided by 12 leaves a remainder of 1 . multiplication) is often called "clock arithmetic". as a clock. The gray slider picks out n and the blue and red sliders pick out a and b to form their sum.

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5+8=1∈Z12 because 5+8=13 and 13 divided by 12 leaves a remainder of 1 . multiplication) is often called "clock arithmetic". as a clock. The gray slider picks out n and the blue and red sliders pick out a and b to form their sum.