- #1
kripkrip420
- 54
- 0
Can someone help me prove that if ab=ac and a does not equal 0, then b=c. You can only use the field axioms. Here is my attempt( I am not sure about the final result).
ab=ac
then,
ab-ac=0
a(b-c)=0
a(0)=0 (Already proved this)
since a cannot equal 0, (b-c) must equal zero and we are left with...
b-c=0
b=c
The only problem I have found with the above is that I have assumed that a does not equal 0. I do not know if this is alright since the statement "a does not equal 0" is part of the originial theorem I am trying to prove.
Thank you to anyone who helps!
ab=ac
then,
ab-ac=0
a(b-c)=0
a(0)=0 (Already proved this)
since a cannot equal 0, (b-c) must equal zero and we are left with...
b-c=0
b=c
The only problem I have found with the above is that I have assumed that a does not equal 0. I do not know if this is alright since the statement "a does not equal 0" is part of the originial theorem I am trying to prove.
Thank you to anyone who helps!