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The key concept here is the notion of equivalence:  in weekday arithmetic, 7 is like 0, because adding 7 is like adding 0.

Since `7  = 0` looks strange, we write `7 equiv 0` .  

Moreover, this is only true if we're using "weekdays" as our basis.  If we're using clock times, then `12 equiv 0` .  This allows us to define modulus functionally:  it's the least positive number equivalent to 0.

Unfortunately, our usual notation for modulus can be confusing for students:  When we write `7 equiv 0 mod 7` , students tend to attach the "mod 7" to the 0, so they think that 7 itself is equal to 0 mod 7.  

What we should write is `7 mod 7 equiv 0 mod 7` .  Or we could write `7 equiv 0` , mod 7 (where separate the "mod 7" with a comma to indicate that it's a dependent clause.  This leads us to `7 equiv 0` , where the modulus is understood (and where we want to end up).