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中学生数学:高中版, ISSN 1003-1901, 2017, Issue 3, pp. 2 - 3
...,常见的还有以待证命题P 的逆否命题、或其推论为逻辑推理依据,或误认为逆命题与原命题等价,转而证明命题的逆命题等等.二、谨防循环论证认识了循环论证,在证明数学命题的过程中,就要避免出现循环论证.而要做到这点,其中一个重要方面是,对命题的证明中所涉依据的与命题逻辑关联要梳理清楚,对所给出的证明过程要注意进行必要地检查琢磨,看看是否犯了循环论证的错误.例2 证明幂函数_,(z)一在[0,+ O<D) 上是增函数.这是人教版A 版必修1中的一道例题,其中一个同学给出了如下不同教材的证明过程:证明任取Lzt,z2∈E0,+oo),且z】<z 2.由于幂函数—lz 在a> 0 时,在[0,十一)上是增函数,所以z <z < ~/=i f(z1)< f(z 2).故幂函数f(x)一~/在[O,+一)上是增函数.剖析细心的同学不难发现,上述证明过程的依据是“幂函数—z。在a> 0时,在[0,+ 一)上是增函数”,即默认了待证的命题正确的前提下,再去证明这个命题.这就犯了循环论证的逻辑错误.正确的证明如下:任取zl,z 2∈E0,+ ∞),且z1< z 2,f(z1)一f(z 2)一~/zl一√... 
同学 | 逻辑错误 | 有理 | 论据 | 严密性 | 证明过程 | 循环论证 | 数学命题
Journal Article
1975, Tai 1 ban., Zhongguo fang zhi cong shu. Hua zhong di fang, Volume di 357 hao, 4 v. (1418 p., [1] fold. leaf of plates)
Book
1975, Zhongguo fang zhi cong shu. Hua zhong di fang, Volume di 358 hao, 2 v.
Book
Angewandte Chemie International Edition, ISSN 1433-7851, 12/2014, Volume 53, Issue 52, pp. 14326 - 14351
Journal Article
eLife, ISSN 2050-084X, 2014, Volume 3, Issue 3, p. e01659
Journal Article
by 康宇
中学生数学:高中版, ISSN 1003-1901, 2015, Issue 11, pp. 2 - 3
同学们知道,运用数形结合思想解题,是常用的数学思维方法.但是,在构图解题的过程中,由于不慎,出现各种构图失误也屡见不鲜,本文通过实例,拟对几种常见的构图失误情形作出若干概括,权当数学学习中一种提醒. 一、图形失真 图形失真,是指在解题过程中,仅凭简单想象或直觉而出现图形失真,并由此导致解题失误. 
解题过程 | 解题失误 | 失真 | 构图 | 数形结合思想 | 数学思维方法 | 数学学习 | 图形
Journal Article
Proceedings of the National Academy of Sciences - PNAS, ISSN 1091-6490, 2015, Volume 112, Issue 15, pp. 4821 - 4826
Journal Article
RSC advances, ISSN 2046-2069, 2018, Volume 8, Issue 39, pp. 22113 - 22121
...–22121 | 22113 * abc Tiantian Bi, b Jinfang Du b and Xianjuan Pang c Graphene–nickel (G–Ni) composites were in situ fabricated by a powder metallurgy method. The eff... 
FRICTION | MECHANISM | WEAR | METAL | XPS | SPECTRA | CHEMISTRY, MULTIDISCIPLINARY | CARBON NANOTUBES | Polymer matrix composites | Particulate composites | Nanotubes | Tribochemistry | Self lubrication | Powder metallurgy | Graphene | Spectrum analysis | X ray photoelectron spectroscopy | Oxidation | Nickel | Lubrication | Sliding friction | Tribology
Journal Article
Journal Article
Nature medicine, ISSN 1078-8956, 2017, Volume 23, Issue 9, pp. 1063 - 1071
Journal Article
资本市场, ISSN 1008-066X, 2014, Issue 11, pp. 15 - 15
...谨防企业债务危机I文/余永定(i¨SU■’[;i!观察家 会永定中国挂安锚章晴幸豳委囊 融资难、融资贵这个问题,不仅影响到短期经济增长.还隐含着危机的可能性。为什么存在危机的可能性7 首先,当前的企业负债率太高。中国社会科学院的研究数据显示,截至201 2年年底,中国企业债务占GDP的比例是1 1 2%,这是现有数据... 
中国社会科学院 | 数据显示 | 金融机构 | 企业负债率 | 债务危机 | 企业债务 | 融资难 | 经济增长
Journal Article
家庭医药, ISSN 1671-4954, 2015, Issue 2, pp. 18 - 19
Journal Article
Proceedings of the National Academy of Sciences - PNAS, ISSN 1091-6490, 2019, Volume 116, Issue 28, pp. 14319 - 14324
Journal Article
by 付煜
2017, Issue 7
Magazine Article
The Plant cell, ISSN 1532-298X, 2011, Volume 23, Issue 11, pp. 3944 - 3960
Journal Article