Question

Explain, please
I confused between x and [x] in modular Arithmetic.

Answer 1

@ganeshie8

Answer 2

what does [x] signify?

Answer 3

congruent class of x
This is definition:
for \(a, b\in Z\) \(a\equiv b\) (mod n) provided n | (a-b) . I understand this concept
[a] ={r \(\in Z\) | \(r\equiv a\) (mod n)}

Answer 4

I don't get the second one.

Answer 5

Is it not that \(a\equiv b (mod n)\), and b is unique?
for example \(5\equiv 1(mod 2)\) so that 1 is a residue in \(Z_5\)
and what [a] mean?

Answer 6

x is some number, its an element within a congruency class

[x] is specifically the name of the set/class

Answer 7

spose i have a jar of mismatched bolts, and i label it 'bolts'

Answer 8

In \(Z_5\) = { 0,1,2,3,4}
[4] = { r | \(r\equiv 4\) (mod 5)}
so that [4] ={ 4, 9, 14, 19,......} right??

Answer 9

looks good to me

Answer 10

Thank you. No more confuse. :)

Answer 11

might be better as: Z5 = {[0],[1],[2],[3],[4]}

Answer 12

Yes, it is. :)

Answer 13

modular arthmatic is a must

Answer 14

@mathmath333 what do you mean?

Answer 15

lol its useful i meann