- 1、本文档共5页,可阅读全部内容。
- 2、原创力文档(book118)网站文档一经付费(服务费),不意味着购买了该文档的版权,仅供个人/单位学习、研究之用,不得用于商业用途,未经授权,严禁复制、发行、汇编、翻译或者网络传播等,侵权必究。
- 3、本站所有内容均由合作方或网友上传,本站不对文档的完整性、权威性及其观点立场正确性做任何保证或承诺!文档内容仅供研究参考,付费前请自行鉴别。如您付费,意味着您自己接受本站规则且自行承担风险,本站不退款、不进行额外附加服务;查看《如何避免下载的几个坑》。如果您已付费下载过本站文档,您可以点击 这里二次下载。
- 4、如文档侵犯商业秘密、侵犯著作权、侵犯人身权等,请点击“版权申诉”(推荐),也可以打举报电话:400-050-0827(电话支持时间:9:00-18:30)。
查看更多
A ZENO’S PARADOX:
Achilles and the Tortoise
Perhaps Zeno’s paradoxes are the most famous in history. In general, philosophers and historians of Mathematics have understood them as paradoxes against movement, in the sense that Zeno and the school of Elea would have used them to deny the reality of movement, demonstrating its impossibility from a logical point of view (motion in itself would imply logical contradictions). If this were so, one could argue that the world real could not be understood by rational thought, or that truth should be purely ideal and phenomena just misleading appearances, etc., but this is not the problem of Zeno’s paradoxes against movement. Some people took seriously Zeno’s arguments (and do so today, as well, so that from time to time someone would come up with a solution of the paradox of Achilles and the Tortoise, as if the problem was justify the movement - not the search for some error in reasoning ...).
Before proceeding, let’s see Achilles and the Tortoise.
Achilles (a champion in the races) is chasing the Tortoise, to which he has given a head start. He reaches the point where the Tortoise started the race, but in the meantime it has travelled a certain distance. Achilles covers this distance and again, in the meantime, the Tortoise runs a further distance. So, when Achilles arrives at a position already reached by the Tortoise, it reaches an even more advanced, and Achilles will never overtake the Tortoise. This reasoning is tantamount to construct an infinite number of points, such that if ABC are three consecutive points in the series, the Turtle covers the distance BC, while Achilles runs AB. Call Zeno’s succession this endless series of points, and ‘Zeno’s points’ and ‘Zenos instants’ the points and the corresponding moments belonging to the succession. To avoid difficulties, we assume that Achilles and the Tortoise run at constant speed.
To discuss the topic is better to establish some assumptions. Indeed, a paradox is a
您可能关注的文档
- 果汁行业市场调查.ppt.ppt
- 金陵十三钗.ppt-1.ppt
- 认证考试Kano模型的数据统计分析.doc
- 丽水市污染源普查全面普查阶段数据质量核查方案.doc文档.doc
- 商法简答论述[精品].doc
- 弹奏乐器—三弦-课件.ppt
- 地理活动设计方案.doc
- 2014年度新申报表填报实务及填报案例示范讲义.doc
- 毕业论文(设计)-英汉委婉语对比研究.doc
- 2016年小学教务处年度工作总结【可编辑版】.doc
- 山东省威海市2023-2024学年高一年级下册期末考试语文试题及答案.pdf
- 2024-2025学年绥化市高二数学上学期开学考试卷(附答案解析).pdf
- 2024届贵州省贵阳某中学联考高考模拟预测地理试题(含答案解析).pdf
- 2024年公务员考试行测常识判断复习讲义.pdf
- 2024年广东学法考试试题附答案(考场一).pdf
- 2024年人教版八年级物理复习讲义:功 专项训练【五大题型】原卷版.pdf
- 江苏省泰州市高港区等2地2023-2024学年九年级上学期期中语文试题.pdf
- 酒店概论及酒店管理培训考试题库.pdf
- 湖北省旅游类《酒店服务》技能高考历年考试试题库(含答案).pdf
- 泰安市2025年中考一模考试物理试题(A)含解析.pdf
文档评论(0)