## 311 – HW1

January 15, 2015

Go through the first 28 propositions of Book 1 of Euclid’s Elements. Make a list of the unjustified inferences you observe in the proofs.

(Due January 20 at the beginning of lecture.)

Use the axioms of vector space to verify that if $V$ is a vector space over a field $\mathbb F$, then:
1. For any $v\in V$, we have $(-1)v=-v$,
2. For any $v\in V$, we have $0v=\vec 0$, and
3. For any $r\in\mathbb F$, we have $r\vec 0=\vec 0$.