kruby/notes-archive
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

Definition Punctuation

Browse Source
This commit is contained in:
Indigo5684
2025-09-30 13:19:35 -05:00
parent 689382af77
commit e04dac50a6
8 changed files with 11 additions and 11 deletions
Download Patch File Download Diff File Expand all files Collapse all files

6
docs/math/real-analysis/2-reals.md
View File

@@ -21,7 +21,7 @@
2. $\mathbb{N} \subseteq F^+$
3. If $a \in F^+$, then $\frac{1}{a} \in F^+$
**Definition** The order relation $a > b$ and $b < a$ is defined by $a - b \in F^+$.
**Definition**. The order relation $a > b$ and $b < a$ is defined by $a - b \in F^+$.
**Theorem**. If $a, b, c \in F$, then
@@ -76,9 +76,9 @@
2. $|a - b| = |b - a|$
3. $|a - c| \leq |a - b| + |b + c|$
**Definition** A set together with a function satisfying these three properties is known as a *metric space*.
**Definition**. A set together with a function satisfying these three properties is known as a *metric space*.
**Definition** The $\varepsilon$-neighborhood of $a \in \mathbb{R}$, denoted $V_\varepsilon(a)$ is the set of all real numbers $x \in \mathbb{R}$ such that $|x - a| < \varepsilon$. That is,
**Definition**. The $\varepsilon$-neighborhood of $a \in \mathbb{R}$, denoted $V_\varepsilon(a)$ is the set of all real numbers $x \in \mathbb{R}$ such that $|x - a| < \varepsilon$. That is,
$$
V_\varepsilon(a) = (a - \varepsilon, a + \varepsilon)