I have this in my math book.
"... if Sum (i=1, n) A(i)^2 = 0 ..."
In the context, there is absolutely no meaning to the value of Sum (i=1, n) A(i)^2 except when it's zero, and the A(i)'s are real numbers.
Instead, they could say...
"... if A(i) = 0 for any 1 <= i <= n ..."
Why not say it in the second form? It is much simpler and not much more typing, and means exactly the same.
This is not the only example of silly algebraic tricks used inappropriately, I will post more if someone cares and if I find them.
When I was taking algebra in highschool I used to point out easier ways to do certain things. It always turned out right and it was always a lot less figuring. My teacher told me to shut up because she had to teach it the way it was written in the book.
It's like using big words when they aren't necessary - it makes whoever wrote it feel smart and seem credible.
Quote from: Yoni on June 27, 2004, 08:57 PM
I have this in my math book.
"... if Sum (i=1, n) A(i)^2 = 0 ..."
In the context, there is absolutely no meaning to the value of Sum (i=1, n) A(i)^2 except when it's zero, and the A(i)'s are real numbers.
Instead, they could say...
"... if A(i) = 0 for any 1 <= i <= n ..."
Why not say it in the second form? It is much simpler and not much more typing, and means exactly the same.
To me, it doesn't seem to mean the same.
Other than that, the squared sum might be more logical and easier to understand for the author.
It could for example be a slight simplification of ||A|| = 0, ||A|| being sqrt(A . A), and the simplification being to make it ||A||^2 = 0 or A . A = 0 or sum(A(i)*A(i)) = 0.