{"resolved":true,"match_type":"uuid","source_type":"original_book","book_id":"38270854-596f-4a26-8183-db8c968c6020","title":"编码 隐匿在计算机软硬件背后的语言","author":null,"edition":null,"publisher":null,"year":null,"isbn":"9787121181184","requested_by":"printed_page","book":{"source_type":"original_book","book_id":"38270854-596f-4a26-8183-db8c968c6020","id":"38270854-596f-4a26-8183-db8c968c6020","uuid":"38270854-596f-4a26-8183-db8c968c6020","title":"编码 隐匿在计算机软硬件背后的语言","normalized_title":"编码隐匿在计算机软硬件背后的语言","author":null,"edition":null,"publisher":null,"year":null,"isbn":"9787121181184","isbns":["9787121181184","0123456789","6044921875","3039331000","0000000000","0000000000000"],"parsed":true,"ai_readable":true,"document_type":"book","page_count":438,"navigation_url":"https://workshop.closeclaw.top/ai/book/38270854-596f-4a26-8183-db8c968c6020","title_url":"https://workshop.closeclaw.top/ai/title/%E7%BC%96%E7%A0%81%20%E9%9A%90%E5%8C%BF%E5%9C%A8%E8%AE%A1%E7%AE%97%E6%9C%BA%E8%BD%AF%E7%A1%AC%E4%BB%B6%E8%83%8C%E5%90%8E%E7%9A%84%E8%AF%AD%E8%A8%80","fixed_page_url_template":"https://workshop.closeclaw.top/ai/book/38270854-596f-4a26-8183-db8c968c6020/page/{printed_page}","path_api_url_template":"https://workshop.closeclaw.top/api/ai/book/38270854-596f-4a26-8183-db8c968c6020/page/{printed_page}","read_url":"https://workshop.closeclaw.top/api/ai/read/38270854-596f-4a26-8183-db8c968c6020","page_url":"https://workshop.closeclaw.top/api/ai/books/38270854-596f-4a26-8183-db8c968c6020/page","search_url":"https://workshop.closeclaw.top/api/ai/books/38270854-596f-4a26-8183-db8c968c6020/search"},"page":{"printed_page":96,"pdf_page":112,"physical_index":112,"physical_index_base":0,"printed_page_status":"recognized","page_sha256":"77bf278c1359fb09e1365a48621af91b78d05e23915edd19f408ebeb29b25826"},"chapter":"编码隐匿在计算机软硬件背后的语言","content":"$$\nF \\times F = F\n$$\n\n这个表达式很明确地表达了布尔代数的意义；母猫和母猫的交集依然是母猫。但是如果F代表的是数字，这个表达式就不会成立。布尔认为式子：\n\n$$\n\\scriptstyle x ^ { 2 } = X\n$$\n\n就是将其代数同传统代数区别开的一条语句。另一个在传统代数中看起来比较有趣的式子是：\n\n$$\nF + F = F\n$$\n\n母猫和母猫的并集依然是母猫。\n\n布尔代数提供了一种解决亚里士多德三段论的数学方法。我们再看看最著名的三段论法中的前两句，但是现在不区分性别：\n\n$$\n\\begin{array} { c } { { \\hbar \\hbar \\uparrow \\hbar \\uparrow \\uparrow \\downarrow \\downarrow \\downarrow \\downarrow \\downarrow } } \\\\ { { \\nonumber } } \\\\ { { \\nRightarrow \\hbar \\downarrow \\hbar \\downarrow \\downarrow \\downarrow \\downarrow \\downarrow \\downarrow \\downarrow \\downarrow \\downarrow \\downarrow } } \\\\ { { \\nmid \\hbar \\uparrow \\downarrow \\downarrow \\downarrow \\downarrow } } \\end{array}\n$$\n\n我们用P表示所有人的集合，M表示必有一死的事物，S表示苏格拉底的集合。\n\n“所有人都难逃一死”是什么意思？意思就是说所有人的集合与必有一死的事物的交集是所有人：\n\n$$\n\\pmb { P } \\times \\pmb { M } = \\pmb { P }\n$$\n\n命题 $\\pmb { P } \\times \\pmb { M } = \\pmb { M }$ 是错误的，因为，在必有一死的事物中，还包含猫、狗和榆树等。\n\n“苏格拉底是人”这句话的意思就是苏格拉底的集合（一个很小的集合）与所有人的集合（一个很大的集合）的交集是苏格拉底：\n\n$$\n\\pmb { S } \\times \\pmb { P } = \\pmb { S }\n$$\n\n根据第一个等式我们可以得到 $\\pmb { P } = \\pmb { P } \\times \\pmb { M }$ ，我们将这个等式带入到第二个等式中去：\n\n$$\n\\pmb { S } \\times ( \\pmb { P } \\times \\pmb { M } ) = \\pmb { S }\n$$\n\n根据结合律，可以写为：\n\n编码—隐匿在计算机软硬件背后的语言\n\n96","previous_page":95,"next_page":97}