Hi! I'm a fourth year majoring in Economics and Data Science, and minoring in Statistics. I'm from the Bay Area and went to high school in Albany, the city right next to Berkeley. I enjoy cooking and eating food and recently got very interested in coffee making.

Beside Math 104, this semester I'm taking CS 189 (CDSS offering) and STAT 230A.

• Natural numbers, $\mathbb{N} = \{0, 1, 2, 3, …\}$
• Integers, $\mathbb{Z} = \{… -1, 0, 1, …\}$
• Rational Numbers, $\mathbb{Q} = \{\frac{m}{n} | m,n \in \mathbb{Z}, n \neq 0\}$
• $\mathbb{Q}$ problematic because a bounded subset might not have a “most economical” upperbound in $\mathbb{Q}$
• $\sqrt{2}$ is not a rational number because there exists no such $m, n \in \mathbb{Z}$ such that $\frac{m}{n} = \sqrt{2}$

HW1: math104_homework1.pdf

HW2: math104_homework2.pdf

HW3: math104hw3.pdf

HW4: math104_hw4.pdf

Questions:

When we modify the rational numbers such that it appears like we are only accessing a certain part of them - why is it still able to get arbitrarily close to any real number?

Since the rationals are infinite based on the denseness of $\mathbb{Q}$, any specific