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Definition Punctuation

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Nathan Nguyen
2025-02-09 22:37:28 -06:00
parent fdafcb0009
commit dd06e549b1
8 changed files with 11 additions and 11 deletions
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docs/math/real-analysis/2-reals.md
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@@ -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)