Help with axiom (1 Viewer)

[withoutaface]

Can someone help me with b), it's driving me insane:S

Thanks

 

[turtle_2468]

If z is not zero then there exists a c (in F) s.t. cz=zc=1. (property of field)
If xz=yz, then xzc=yzc
So x=y as req'd.

 

[withoutaface]

If z is not zero then there exists a c (in F) s.t. cz=zc=1. (property of field)
If xz=yz, then xzc=yzc
So x=y as req'd.

Thanks a lot. Slide Rule, you win this round

 

[Slidey]

Arr, pirates bold be we.

 

[turtle_2468]

?? Is this a competition to see whether someone would answer a q or something?

 

[withoutaface]

?? Is this a competition to see whether someone would answer a q or something?

Nah it was that he gave me a solution, and I thought by multiplying both sizes by z^-1 it was assuming what you had to prove

 

[turtle_2468]

Well you're assuming the uniqueness of z^-1 (easily provable, I'll leave it as an exercise )
But quibbles aside that works too..

 

[Arkad]

I hate the books that say: I'll leave it as an exercise. It's just a poor excuse to save paper and ink.

ab=ba=1, ac=ca=1

b=b(1)=b(ac)=(ba)c=(1)c=c

therefore b=c.

I'll leave it as an exercise for you to identify the field axioms I've used. HAHA.

 

[turtle_2468]

Or, to be more honest, that it's well known but I'm too lazy to prove it right now.. actually considering the age of the post, right then..

I hate the books that say: I'll leave it as an exercise. It's just a poor excuse to save paper and ink.

ab=ba=1, ac=ca=1

b=b(1)=b(ac)=(ba)c=(1)c=c

therefore b=c.

I'll leave it as an exercise for you to identify the field axioms I've used. HAHA.

 

[Arkad]

I'm too lazy to prove it right now...

That's exactly my point, why can't there be a book which proves everything? All the writers are lazy and cheap, they always use funny excuses such as "leave you as an exercise".

 

[turtle_2468]

That's exactly my point, why can't there be a book which proves everything? All the writers are lazy and cheap, they always use funny excuses such as "leave you as an exercise".

because then you'd be complaining about all the irrelevant (ie don't need for HSC) stuff you have in the textbook which pushes the price up by another $5...

 

[Arkad]

Okay, I won't complain.