The Unapologetic Mathematician

Mathematics for the interested outsider

Additive Functions

I’ve got internet access again, but I’m busy with a few things today, like assembling my furniture. Luckily, Tim Gowers has a post on “How to use Zorn’s lemma”. His example is the construction of additive (not linear) functions from \mathbb{R} to itself.

In practice, as he points out, this is equivalent to defining linear functions (not just additive) from \mathbb{R} to itself, if we’re considering \mathbb{R} as a vector space over the field \mathbb{Q} of rational numbers! This is a nifty little application within the sort of stuff we’ve been doing lately, and it really explains how we used Zorn’s Lemma when we showed that every vector space has a basis.

August 12, 2008 Posted by | Algebra, Linear Algebra | 9 Comments