The reals form a field.

https://en.wikipedia.org/wiki/Real_number

Bob

]]>the field is in the ring and the ring is in the group

i don't know how to write the mathematic definition by my own because i just understand it ... it's not a biology to save it ...

well ... i copied these definition from a site i hope it's useful for youGroup:

Group is the most fundamental and pervasive notion of the Higher or Abstract Algebra. It's a set along with a single operation defined on its elements. The group is called additive if the symbol for the operation is "+". It's multiplicative if the symbol "·" of multiplication is used instead. But any other symbol can be used as well. There is always a unique element (1, for multiplicative, and 0, for additive, groups) that leaves elements invariant (unchanged) under the defined operation, like a+0=a. Also, for every element a there exists a unique inverse b such that, for example, in the case of the additive symbol, a+b=0 and b+a=0. Most often, however, the inverse is denoted as a-1. Lastly, the group operation must be associative like in a·(b·c)= (a·b)·c. A group is commutative or Abelian if its operation is symmetric, like in a+b=b+a.Ring:

A ring is an additive commutative group in which a second operation (normally considered as multiplication) is also defined. The multiplication must be associative, i.e. a+(b+c)= (a+b)+c and the distributive law a(b + c) = ab + ac and (b + c)a = ba + ca must hold. If a ring is also a commutative multiplicative group (of course, with 0 removed) then it's called a field.Field:

A field is a ring in which multiplication is a group operation. In France (and sometimes elsewhere in Europe), the multiplicative group need not be commutative. In the US and Russia it must be.

Example please!

]]>I already have basic differential and integral calculus down and am starting to learn abstract algebra.

I'm in the same boat. Kind of weird how after doing a few years of calculus you go back to proving why -1 * -1 = 1, isn't it?

]]>But I am studying other subjects that interest me. I already have basic differential and integral calculus down and am starting to learn abstract algebra.

]]>flatulant 13 year old...did that make sense?

And where are you that you are learning group theory in middle school!?

i don't know how to write the mathematic definition by my own because i just understand it ... it's not a biology to save it ...

well ... i copied these definition from a site i hope it's useful for you

Group:

Group is the most fundamental and pervasive notion of the Higher or Abstract Algebra. It's a set along with a single operation defined on its elements. The group is called additive if the symbol for the operation is "+". It's multiplicative if the symbol "·" of multiplication is used instead. But any other symbol can be used as well. There is always a unique element (1, for multiplicative, and 0, for additive, groups) that leaves elements invariant (unchanged) under the defined operation, like a+0=a. Also, for every element a there exists a unique inverse b such that, for example, in the case of the additive symbol, a+b=0 and b+a=0. Most often, however, the inverse is denoted as a-1. Lastly, the group operation must be associative like in a·(b·c)= (a·b)·c. A group is commutative or Abelian if its operation is symmetric, like in a+b=b+a.

Ring:

A ring is an additive commutative group in which a second operation (normally considered as multiplication) is also defined. The multiplication must be associative, i.e. a+(b+c)= (a+b)+c and the distributive law a(b + c) = ab + ac and (b + c)a = ba + ca must hold. If a ring is also a commutative multiplicative group (of course, with 0 removed) then it's called a field.

Field:

A field is a ring in which multiplication is a group operation. In France (and sometimes elsewhere in Europe), the multiplicative group need not be commutative. In the US and Russia it must be.

Can anyone explain the difference between a ring, a group, and a field in a way so that your average 13 year old can understand?

]]>http://en.wikipedia.org/wiki/Group_%28mathematics%29

http://en.wikipedia.org/wiki/Field_%28mathematics%29

]]>