Milo's Math Corner

[KOOPS95]

This thread is for the discussion of anything math related. I want this to be a serious thread, so try not to go off-topic.

To start the discussion, I thought of something while sitting in Geometry today. Well, the Reflexive Property of Equality states that A = A. I thought of a way for A to not equal A! Look below:

A = √(A^2)

Think about this. Any number has two square roots: a negative and positive. Well, let's say that in this case, the A on the right side of the equal sign is negative. If you work it out, you could still get A.

A = √(-A * -A)
A = √(A^2)
A = A.

However, you could also get the result below.

A = √(-A * -A)
A = √(A^2)
A = -A

Does this make any sense at all? Is this a logical argument, or am I just making myself look stupid?

I just learned this in Algebra today, being the lowly Freshman I am.

When you have a number being rooted (i.e. √A^2), if the end product would have an ODD exponent (i.e. when it is rooted, you get A^3, A^5, and so on. A^1 included!), you put absolue value lines around the variable. So, the equation would look something like this;

|A|=√A^2

Then, you get;

|A|= (A) or (-A), which is true.