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 [math]\displaystyle{ a*a^2=1 }[/math] implies [math]\displaystyle{ a=1 }[/math]. --Drorbn 06:16, 22 September 2006 (EDT)

because [math]\displaystyle{ b=a^{-1}=a^2 }[/math], if ab=1, why shouldn't [math]\displaystyle{ a*a^2=1 }[/math]?

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

Finally I'm registered.....ok, if [math]\displaystyle{ a*a^2=1 }[/math], 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 [math]\displaystyle{ a*a^2=1 }[/math] implies [math]\displaystyle{ a=1 }[/math]. --Drorbn 03:24, 23 September 2006 (EDT)

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

Well, OUR very own field has an element [math]\displaystyle{ a }[/math] for which [math]\displaystyle{ a^3=1 }[/math] yet [math]\displaystyle{ a\neq 1 }[/math]... --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 [math]\displaystyle{ a^3=1 }[/math] in a general field does not imply the equality [math]\displaystyle{ a\neq 1 }[/math] --- why would it? After all, [math]\displaystyle{ a^2=1 }[/math] does not imply [math]\displaystyle{ a\neq 1 }[/math] either. Here are two examples for fields in which there is an [math]\displaystyle{ a\neq 1 }[/math] for which [math]\displaystyle{ a^3=1 }[/math]:

1. Our field and our [math]\displaystyle{ a }[/math].
2. The complex numbers [math]\displaystyle{ {\mathbb C} }[/math] and [math]\displaystyle{ a=-\frac12+\frac{\sqrt{3}}{2}i }[/math].

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