# 宇集╱universal set

[集合](/math/set.md) ⟩ 宇集 (universe, universal set, domain of discourse)

{% hint style="success" %}
在討論某特定問題時，規範此問題所牽涉到的<mark style="color:yellow;">**變數所能變動的範圍**</mark>(context)，稱為「<mark style="color:purple;">**宇集**</mark>」
{% endhint %}

{% hint style="warning" %}
雖然我們說：

* 「一個[述詞](/math/logic/predicate.md) $$A(x)$$ 就可以界定一個[集合](/math/set.md) $$A$$」
* 「[集合](/math/set.md)」就是「[述詞](/math/logic/predicate.md)」
* 「$$A(x) = \text{true}$$」代表「$$x\in A$$」

但通常我們會<mark style="color:yellow;">**避免**</mark>說像「$$x^2<5$$」這樣如此「<mark style="color:yellow;">**開放性的敘述**</mark>」，而是會先「界定<mark style="color:yellow;">**變數**</mark>所能變動的<mark style="color:yellow;">**最大範圍**</mark>」，例如：「$$x\in\mathbb{N}$$ ($$x$$ 是自然數) 」 或「$$x\in\mathbb{R}$$ ($$x$$ 是實數) 」等等，這樣的範圍就稱之為「<mark style="color:purple;">**宇集**</mark>」，因為如果沒有做這樣的設定，那麼像「$$x^2<5$$」這樣的敘述到底包含哪些元素，意義上是模糊不清的。
{% endhint %}

{% tabs %}
{% tab title="📗 參考" %}

* [ ] 國家教育研究院 ⟩ [樂詞網](https://terms.naer.edu.tw) ⟩ [宇集\[合\]](https://terms.naer.edu.tw/detail/c81bcae234e179883e4b89c21e34cddc/?startswith=zh\&seq=2)
* [ ] Wolfram ⟩ [MathWorld](https://mathworld.wolfram.com) ⟩ [Universal Set](https://mathworld.wolfram.com/UniversalSet.html)
* [ ] wiki ⟩&#x20;
  * [ ] [Universe (mathematics)](https://en.wikipedia.org/wiki/Universe_\(mathematics\))
  * [ ] [Universal set](https://en.wikipedia.org/wiki/Universal_set)
    {% endtab %}
    {% endtabs %}


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