Proof: I studied Math

For today's blog I decided to give myself a little bit of a challenge. You see, I wrote a whole book review on a mathematical novel and described how the subject was so enticing that I had to study it. However, as I am sure many of you relate to, I do not find myself using the greulling higher level mathematics in my everyday life. Therefore, I chose a handful of theorems I found in my old notebooks and gave my best effort to see if I could still prove them. I am pretty sure that these proofs hold, however, please feel free to peer review and disagree. Since I cannot figure out how to Latek directly on the blog interface, I have linked the PDF here.

I mean it - please disagree with me. It will only be more telling of my knowledge if I can defend these. Perhaps for tomorrow's blog I will find the solutions and correct my own work, if any correction needs to be done.