Talk:06-240/Homework Assignment 1

What information should be included on the homework assignments besides the answers to the assignment? Is student name, Math 240, Homework Assignment 1 and date sufficient? MC

Yes. --Drorbn 14:50, 15 September 2006 (EDT)

Q4

i have a question on Q4. for the part a^-1=a^2, if it's true, then a*a^2=1, which makes a=1....but a can't be 1 right?

I don't see why $a*a^{2}=1$ implies $a=1$. --Drorbn 06:16, 22 September 2006 (EDT)

because $b=a^{-1}=a^{2}$, if ab=1, why shouldn't $a*a^{2}=1$?

But what's wrong with that? --Drorbn 17:16, 22 September 2006 (EDT)

Finally I'm registered.....ok, if $a*a^{2}=1$, then a=1,but a field cannot have identical elements.....or can it?.........btw why is your name shown here but mine not?...never used a wiki based site....

Repeat: I don't see why $a*a^{2}=1$ implies $a=1$. --Drorbn 03:24, 23 September 2006 (EDT)

er....since $a*a^{2}=a^{3}=1$, or am I right about $a*a^{2}=a^{3}$?....and what makes $a^{3}=1$ except a=1?...sorry but please tell me where I got wrong.........

Well, OUR very own field has an element $a$ for which $a^{3}=1$ yet $a\neq 1$... --Drorbn 17:08, 23 September 2006 (EDT)

ok.....that's....very...convincing......I'll shut up...

You seem unhappy, but I actually meant what I said. The equality $a^{3}=1$ in a general field does not imply the equality $a\neq 1$ --- why would it? After all, $a^{2}=1$ does not imply $a\neq 1$ either. Here are two examples for fields in which there is an $a\neq 1$ for which $a^{3}=1$:

1. Our field and our $a$.
2. The complex numbers ${\mathbb {C} }$ and $a=-{\frac {1}{2}}+{\frac {\sqrt {3}}{2}}i$.

--Drorbn 17:38, 24 September 2006 (EDT)

Actually I guessed it had something to do with the field. But this concept is still new to me, I just can't convice myself a is not 1 when a*a*a=1...But that example of complex numbers is indeed very convincing....thank you for your patience :)