As part of Sharpening the Saw I’m going to start writing about things I’m studying. To get started I wanted to make a post with some mathematics notation. It will be a good way to make sure all the pieces are in place.

First, one of my favorite equations: \(y = mx + b\).

Now for something a bit more complex:

\[\begin{align} x=\frac{-b\pm \sqrt{b^2-4ac}}{2a} \end{align}\]

Thanks to the hard work of the folks behind MathJax it was very easy to add mathematical equations to my blog.

Proof That One Equals Zero (Not-Really)

Given that \(a\) and \(b\) are integers such that \(a=b+1\), prove that \(1=0\).

\[\begin{align} a &= b + 1 && \text{Given} \\ (a-b)a &= (a-b)(b+1) && \text{Multiplication Prop. of =} \\ a^2 - ab &= ab + a - b^2 - b && \text{Distributive Prop.} \\ a^2 - ab - a &= ab + a - a - b^2 - b && \text{Subtraction Prop. of =} \\ a(a-b-1) &= b(a - b 1) && \text{Distributive Prop.} \\ a &= b && \text{Division Prop. of =} \\ b+1 &= b && \text{Transitive Prop. of =} \\ Therefore, 1 &= 0 && \text{Subtraction Prop. of = } \\ \end{align}\]