---
description: real number system╱🚧 under construction
---

# 實數系定義

[數學](../../../../math) ⟩ [數系](../../..) ⟩ [實數](../..) ⟩ [建造](..) ⟩ [定義實數]() ⟩ 實數系定義

{% hint style="success" %}
![](https://487293287-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F-M5-JmwIjjSzWft9bo8C%2Fuploads%2F6psqPGgFHguzM4yqLGH2%2Fdefinition%2081x31.png?alt=media\&token=4023cbcf-b720-4ff9-b90d-5fe6550be85e) 定義「<mark style="color:purple;">實數系</mark>╱<mark style="color:yellow;">real number system</mark>」，以 $${\color{orange}\mathbb{R}}$$ 代表：

$${\color{orange}\mathbb{R}} =$$ { $${\color{orange}a}$$ | $${\color{orange}a}$$ 是[戴德金分割](dedekind-cut) }

並稱每一個「[戴德金分割](dedekind-cut)」為「<mark style="color:purple;">實數</mark>╱<mark style="color:yellow;">real number</mark>」。
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{% tabs %}
{% tab title="🔴 主題" %}
* [rational](rational "mention")
* 🚧 存在不是 (-∞, r) 形的[戴德金分割](dedekind-cut)
{% endtab %}

{% tab title="👥 相關" %}
* <mark style="color:yellow;">**推論**</mark>：
  * [order](../order "mention")
  * [add](../add/add "mention")
  * [negative](../add/negative "mention")
{% endtab %}

{% tab title="🗺️ 圖表" %}
<img src="https://487293287-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F-M5-JmwIjjSzWft9bo8C%2Fuploads%2FhUAU48BVJtxSlZNMTOhU%2Fdedekind_dc1.svg?alt=media&#x26;token=e7d49102-ea11-48d9-8ca6-969ec8ab2201" alt="" class="gitbook-drawing">

<img src="https://487293287-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F-M5-JmwIjjSzWft9bo8C%2Fuploads%2Fp2u2CzV56lFCyEPJkB5E%2Fdedekind.dc2.svg?alt=media&#x26;token=332a1083-34ac-43c7-95d6-c7c764e50106" alt="" class="gitbook-drawing">

<img src="https://487293287-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2F-M5-JmwIjjSzWft9bo8C%2Fuploads%2FhU6PH56Wl9OXmQKUoUdE%2Fdedekind.dc3.svg?alt=media&#x26;token=5ffe9fbb-69ca-4254-ac90-ea627d1378c2" alt="" class="gitbook-drawing">


{% endtab %}

{% tab title="📗 參考" %}
* [ ] Understanding Analysis ⟩ 8.6 A Construction of R From Q
* [ ] wiki ⟩ [Dedekind cut](https://en.wikipedia.org/wiki/Dedekind_cut)
{% endtab %}
{% endtabs %}
