Please help me... Determine which, if either, of the following sets form a group with respect to the given operation.
I. {0, 1, 2, 3, 4}; addition modulo 5
II. the set of integers with respect to addition.

Question

Please help me... Determine which, if either, of the following sets form a group with respect to the given operation.
I. {0, 1, 2, 3, 4}; addition modulo 5
II. the set of integers with respect to addition.

terenzreignz · Answer

Let's have a look at the first set :D
{0,1,2,3,4} the set of nonnegative integers less than 5.
When you add any of them and take the result at modulo 5, is it still going to be in that set?

anonymous · Answer

ok

anonymous · Answer

so like, 3+2 = 5

terenzreignz · Answer

nu-uh... remember, after adding, you take the result modulo 5, and what's 5(mod 5) = ?

anonymous · Answer

5

terenzreignz · Answer

no...

anonymous · Answer

hum this is were I don't understand

terenzreignz · Answer

Recall modulo... a number modulo 5 is the remainder if you divide said number by 5.

If you divide 5 by 5, what's the remainder?

anonymous · Answer

1

terenzreignz · Answer

Really? When last I looked, 5 was divisible by 5 :P

anonymous · Answer

oh duh. sorry

terenzreignz · Answer

Let's give that set a name, for future reference:
$$\Large \mathbb{Z}_5=\{0,1,2,3,4\}$$

anonymous · Answer

thats right because we are using algebra

terenzreignz · Answer

now, when you add any two elements of $\large \mathbb{Z}_5$ and then get the result, modulo 5, is that result still going to be in $\large \mathbb{Z}_5$?

anonymous · Answer

this is all new to me

terenzreignz · Answer

I just gave it a name, don't worry. Now, my question ^
Please give it a good think...

anonymous · Answer

ok

anonymous · Answer

yes

terenzreignz · Answer

How do you know?

anonymous · Answer

Because we are dividing Z5 by Z5 and it divisible.

terenzreignz · Answer

not a very clear reason, is it? :)

anonymous · Answer

no

terenzreignz · Answer

Look, when you're dividing by 5 and getting remainders, it has to be one of 0,1,2,3,4
any more than that, it won't make sense as a remainder, yeah/

anonymous · Answer

yeah

anonymous · Answer

so that means that both form a group

terenzreignz · Answer

We haven't even gone to the second item yet, slow down LOL
The rest is easy though... is addition associative?

anonymous · Answer

lol

anonymous · Answer

are u good with symmetry because I have no idea how to do that and my next 6 questions is on that

terenzreignz · Answer

never heard of them :)

anonymous · Answer

yeah me either :)

anonymous · Answer

so was i right about that they both form a group