How can this (math) be?

[glatt]

Originally Posted by tw

(a+b)(a-b) = b (a-b)
a+b = b

To get from (a+b)(a-b) = b (a-b)
to
a+b = b
you must divide each side by (a-b). That's great, except...

since a=b, then (a-b) = (a-a) = 0

Only Chuck Norris can divide by zero.

[tw]

Originally Posted by glatt

since a=b, then (a-b) = (a-a) = 0

It is called the trivial solution.
a * c = b * c
has a unique solution (for real numbers) EXCEPT when c = 0. We tend to forget the other part of that algebraic relationship: that c cannot equal 0. Once c becomes zero, then any number can equal any other.

Naive will then proclaim that math can be manipulated - another interpretation of "lie, damn lies, and statistics". Instead, by providing only a half fact (by forgetting the part where c cannot equal zero), then a mistake occurs.

c=0 is called the trivial solution; an overlooked mathematical error that glatt has successfully identifed.

[glatt]

Originally Posted by tw

an overlooked mathematical error that glatt has successfully identifed.

To be fair, Happy Monkey beat me to it. I just didn't see his solution because he hid it behind a white font color. It wasn't until Beestie quoted him later that I saw his entire post.