## Errata

• Theorem 2.1 contains a typo. The correct statement is

If $$a_n \leq b_n \leq c_n$$, for all $$n$$ and

$$\lim_{n \rightarrow \infty} a_n = \lim_{n \rightarrow \infty} b_n = L$$

then

$$\lim_{n \rightarrow \infty} c_n = L$$.

• Chapter 2, Application 20 should state that the minimum terms desired are $$n = 0,1$$ and $$2$$.
• Chapter 2, Exploration 46 is missing a condition. The set in item 4 of this exploration should be $$S = \{x \in \mathbb{R} | x = 1/n, n \in \mathbb{Z} \setminus \{0\}\}$$
• Chapter 2, Exploration 58 indicates the dots are green and red. The dots on the website have been changed to accomodate color-blind students. The color relationship is described in each exploration.
• Chapter 2, Conjecture 60 should refer to the sequence of supremums $$\{v_N\}$$.
• Chapter 6, Explorations 2-8 should be Applications 2-8.
• Definition 7.2 contains a typo. The correct version is below.

Let $$X$$ be a metric space with metric $$d$$ and suppose $$U,\, V \subset X.$$ A set $$U$$ is dense in a set $$V$$ if for every $$\epsilon>0$$ and every point $$v \in V$$, there exists a $$u \in U$$ such that $$d(u,v)< \epsilon$$.