Math Wisdom

Today a professor said something that almost made sense in the real world:

If you don't have an identity element then its hard to be a group.

A group is a set (e.g. the integers) with an operation (e.g. addition) that behaves nicely. In particular, it has to have an identity. In our example, that would be zero: zero + something gives you something back again.

In the real world, groups are made up of people who want to change. Political groups want to change government, churches want to reform individuals, clubs want to learn new skills. But to be successful every group has to start with a baseline something that they share in common. Alright, so this isn't a really deep thought or anything. But it was something in a topology class that almost made sense. It deserved to be remembered.