Give a one-paragraph real-world description as a motivation for mod seven arithm

Question

Give a one-paragraph real-world description as a motivation for mod seven arithmetic using days of the week, similar to the way clock arithmetic is a motivation for mod twelve arithmetic. Describe how you would make a natural definition of addition on your number system, and talk about how mod seven arithmetic illustrates the fact that 6 days after a Friday is a Thursday. (Hint: assign the symbols in mod seven to an appropriate choice of days of the week; you can pick whatever you want to correspond to day 0.)

Explanation / Answer

There are seven days in a week. We know that every 7 days, we will get the same day of the week.
Suppose you start from Monday, 2 days after Monday is Wednesday, we can write it as
Monday + 2 = Wednesday.

Now, 3 days after Wednesday is Saturday, so we can write it as
Wednesday + 3 = Saturday.

2 days after Saturday is Monday, so we will write
Saturday + 2 = Monday.

Now denote the days like this:
Monday = 0
Tuesday = 1
Wednesday = 2
Thursday = 3
Friday = 4
Saturday = 5
Sunday = 6

Then suppose you wish to know the day it is after 100 days if it is a Monday today.
Find 100(mod 7), we get 2.
See from the table that the corresponding day is Wednesday.

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