- #1
kripkrip420
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Hi there! I have been reading Apostol's "Calculus: Volume 1" and have been trying to prove a few theorems using specific field axioms(note that this is not a "homework" question since I have not been assigned it, but instead, chosen to attempt it out of curiosity). Although I am not a math major, I am interested in these proofs. The theorem follows as such;
Given a and b and a does not equal zero, there exists one such x that x=b/a. This is called the quotient...etc.
Can someone help me prove the above theorem using the field axioms? I am not sure where to start.
My attempt...
ax=b
choose one y such that ax(y)=1
then,
ax(y)=b(y)=1
and I get stuck there.
Please help me if you can! Thank you in advance!
Given a and b and a does not equal zero, there exists one such x that x=b/a. This is called the quotient...etc.
Can someone help me prove the above theorem using the field axioms? I am not sure where to start.
My attempt...
ax=b
choose one y such that ax(y)=1
then,
ax(y)=b(y)=1
and I get stuck there.
Please help me if you can! Thank you in advance!