3.1 Part 2

1. What was the most difficult part of the material for you?
The most difficult part of this reading for me was the part that talked about subrings and subfields. I'm still not exactly sure what the difference is between the two. I mostly think I got confused with the example on page 49 where it says "Z is a subring of the ring Q of rational numbers and Q is a subring of the field R of all real numbers. Since Q is itself a field, we say that Q is a subfield of R." It could be because I'm not exactly sure what a "field" is that they are referring to here. Is it like a vector field? I'm not sure. I'm also confused why they aren't just saying that Q is a subring of R..... you know? I'm confused.

2. Find out what the heck a "field" is here, and write about it  :)
 I found a site on the internet that said the following: "A field is a ring, such that for any a that is not equal to 0, there is an element b that is inverse to a with respect to multiplication: ab=1." So, I'm guessing that since in Q we could say that a=2, and then b=1/2 and they are both in Q and ab=1. So, I guess that answers my questions, but I don't know why they don't just call it a ring and make my life easier.