{"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":95,"pdf_page":111,"physical_index":111,"physical_index_base":0,"printed_page_status":"recognized","page_sha256":"c59c8358b6b5d930f2f843e0d26f2c83fbc984db1dae6011d48d235066858619"},"chapter":"编码隐匿在计算机软硬件背后的语言","content":"$$\n1 - M = F\n$$\n\n另一个要用到的符号就是0，在布尔代数中，符号0表示空集一不包含任何元素的集合。空集往往是两个互斥集合的交集，例如，母猫与公猫的交集：\n\n$$\n\\pmb { F } \\times \\pmb { M } = 0\n$$\n\n注意，在布尔代数中，1和0有时也同在传统代数中的应用一样。例如，所有猫与母猫的交集是母猫的集合：\n\n$$\n1 \\times F = F\n$$\n\n空集与母猫的交集还是空集：\n\n$$\n0 \\times { \\pmb F } = 0\n$$\n\n空集与母猫的并集则是母猫：\n\n$$\n0 + F = F\n$$\n\n但是有时也会出现与传统代数相悖的结果。例如，所有猫与母猫的并集是所有猫的集合：\n\n$$\n1 + F = 1\n$$\n\n这个式子在传统代数中就是没有意义的。\n\n由于F是母猫的集合，（1-F）是所有非母猫的猫的集合，因此这两个集合的并集是1:\n\n$$\nF + ( 1 { - } F ) = 1\n$$\n\n而这两个集合的交集为0：\n\n$$\nF \\times ( 1 - F ) = 0\n$$\n\n在历史上，这个公式代表了逻辑学上的一个重要概念：这一概念被称为矛盾律。矛盾律指出事物不可能既是它本身，同时又是它的对立面。\n\n布尔代数中与传统代数形式上最大区别之处就是这样一个表达式：\n\n10 逻辑与开关\n\n95","previous_page":94,"next_page":96}