Number theory. What does the notation ℤ/nℤ mean?

Question

it says a set of equivalence classes modulo n?

so if n = 3
ℤ/nℤ = { [0] , [1], [2] }
= { {... -6,-3,0,3,6...} , {...-5,-2,1,4,7...} , {...-5,-1,2,5,8,...} }

so basically it's a set of sets?

Answer 1

Basically, yea. They're borrowing a notation from Group Theory (Abstract Algebra). I could get more into groups and rings and quotient groups, but I think it'd confuse you and it's not completely relevant to know the underlying structure to understand the number theoretic implications.



There's also an equivalent notation you'll run into which is ℤ_n (ℤ with a subscript n). I've seen this much more often than the given quotient group notation.





The set is special because you can actually define addition and multiplication on the elements.

[a] + [b] = [a + b]

[a][b] = [ab]



This (and other stuff) is what makes these things a ring. You'll notice these are the congruence relation properties

if

a ≣ b (mod n)

c ≣ d (mod n)



then

a+c ≣ b+d (mod n)

ac ≣ bd (mod n)

Answer 2

medical notation = A x 10 ^ B A will continually could be between a million - 10 so in case you have a huge form like ninety two,000 you may positioned it as 9.2 (between a million-10) x 10 to the flexibility of four given which you count huge form the numbers from the . to the final 0

Answer 3

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