Re: [其他] 零為甚麼在空集合裡面

看板Math作者china2025 (2025全面小康)時間8年前 (2018/01/21 19:00)推噓1(1推 0噓 22→)

留言23則, 5人參與討論串2/2 (看更多)

※ 引述《china2025 (2025全面小康)》之銘言： : 我是自修學哲學分析哲學 : 裡面提到用邏輯概念去區分自然數 : 一個東西和自己一樣 : 一個東西和自己不一樣 : 用以上兩個東西去分類自然數 : 空集合就是一個東西和自己不一樣的集合 : 那請問 : 零不是和自己一樣嗎 : 零為甚麼會在空集合中 : ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ : 我是完全外行寫錯請見諒 : 該數學作者是Frege The obvious suggestion is then to identify the first of the natural numbers, namely, the number 0, with the null class. This is what is done in modern set theory and is the simplest definition. Frege, in fact, offers a more complicated definition, identifying the number 0 not directly with the null class but with the class of classes that have the same number of members as the null class; but we can ignore this complication here. For present purposes, let us accept that this gives us our first natural number, the number 0, defined as the null class. We can then form the concept “is identical with 0” (i.e., the concept “is identical with the null class”). Here the corresponding class has just one member, namely, 0 (the null class itself), since only this object (i.e., 0) is identical with 0. This class (the class of things that are identical with 0) is distinct from its sole member (0, i.e., the null class), since the former has one member and the latter has no members, so we can identify the number 1 with this class (the class of things that are identical with 0). We now have two objects, and can then form the concept “is identical with 0 or 1” (using, in this case, the additional logical concept of disjunction). This gives us a corresponding class which we can identify with the number 2, and so on. Starting with the null class, then, and using only logical concepts, we can define all the natural numbers. Beaney, Michael. Analytic Philosophy: A Very Short Introduction (Very Short Introductions) (pp. 13-14). OUP Oxford. Kindle Edition. -- ※ 發信站: 批踢踢實業坊(ptt.cc), 來自: 118.160.90.111 ※ 文章網址: https://www.ptt.cc/bbs/Math/M.1516532424.A.10A.html

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china2025

01/21 19:01, 8年前 , 1^F

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