[Math] interval (구간)

Definition

A (real) interval is a set of real numbers that contains all real numbers lying between any two numbers of the set.

구간(interval)을
parentheses와 square bracket을 이용하여 표현
하는 것을 꼭 기억할 것.

---

종류

An open interval (개구간) does not include its endpoints, and is indicated with parentheses.

For example,

• $(0,1)$ means greater than $0$ and less than $1$.
• This means $(0,1) = \{x | 0 < x < 1\}$.

---

A closed interval (폐구간) is an interval which includes all its limit points, and is denoted with square brackets.

For example,

• $[0,1]$ means greater than or equal to $0$ and less than or equal to $1$.

---

A half-open interval (반개구간=반폐구간) includes only one of its endpoints, and is denoted by mixing the notations for open and closed intervals. 

For example, 

• $(0,1]$ means greater than $0$ and less than or equal to $1$, while 
• $[0,1)$ means greater than or equal to $0$ and less than $1$.

---

참고

• A degenerate interval (퇴화구간??) is any set consisting of a single real number (i.e., an interval of the form $[a,a]$).
• Some authors include the empty set in this definition.
• A real interval that is neither empty nor degenerate is said to be proper, and has infinitely many elements.

---

Reference

https://en.wikipedia.org/wiki/Interval_(mathematics)

Interval (mathematics) - Wikipedia

https://dsaint31.github.io/math/math-week03/

[Math] Week 03

---