Proofs

Proofs have been an integral part of mathematics since the Ancient Greeks. They can be thought of as a logical arguments for proving a mathematical statement based on assumptions and known relationships. A good proof should be elegant, easy to follow and should stand up to testing. This can be very intimidating for beginners (which is what we are in CSC165). But, if you know how to structure a proof, then there's always a place to start and a good structure can facilitate ideas and insight. Since I am a visual thinker, I going to compare the structure of a proof to matryoshka dolls (cheesy, I know).

Another name for matryoshka dolls is Russian nesting dolls because each smaller doll is contained in a bigger doll. The smallest doll is proof essence of the proof, the part that requires insight and can be tricky. The outer dolls contain that insight and apply it to domains where the relationship is true. I've illustrated a proof structure from last week's tutorial to show what I mean.

If you are comfortable creating the structure of a proof, then you can spend more energy on the little doll. More on how to go about proving the mathematical relationship contained by the small doll in my next post.