/sci/ - Science & Math

I provided the entire proof for the sake of context but really only one part matters.
Why can we write the division with |r| Is less than c/2
I understand that the Euclidean algorithm shows that there's r with absolute value less than c, so how can we just make this assertion

I provided the entire proof for the sake of context but really only one part matters.
Why can we write the division with |r| Is less than c/2
I understand that the Euclidean algorithm shows that there's r with absolute value less than c, so how can we just make this assertion

I don't know if anybody will actually read through pic related but why can you assert that there are q and r such that r is less than |c|/2.
I thought Euclidean division could only show that it's less than |c|