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In mathematics, a singularity is in general a point at which a given mathematical object is not defined, or a point where the mathematical object ceases to be well-behaved in some particular way, such as the lack of differentiability or analyticity.

In mathematics, a singularity is in general a point at which a given mathematical object is not defined, or a point where the mathematical object ceases to be well-behaved in some particular way, such as the lack of differentiability or analyticity.

在数学中，<font color="#ff8000">奇点 singularity</font>一般是一个给定数学对象没有定义的点，或一个数学对象在某些特定方面不再表现良好的点，例如缺乏可微性或可分析性。

在数学中，<font color="#ff8000">奇点 singularity</font>一般是一个给定数学对象没有定义的点，或一个数学对象在某些特定方面不再表现良好的点，例如缺乏可微性或可分析性。<ref name=":0">{{Cite web|url=https://mathvault.ca/math-glossary/#singularity|title=The Definitive Glossary of Higher Mathematical Jargon — Singularity|last=|first=|date=2019-08-01|website=Math Vault|language=en-US|url-status=live|archive-url=|archive-date=|access-date=2019-12-12}}</ref><ref name=":1">{{Cite web|url=http://mathfaculty.fullerton.edu/mathews/c2003/SingularityZeroPoleMod.html|title=Singularities, Zeros, and Poles|website=mathfaculty.fullerton.edu|access-date=2019-12-12}}</ref><ref>{{Cite web|url=https://www.britannica.com/topic/singularity-complex-functions|title=Singularity {{!}} complex functions|website=Encyclopedia Britannica|language=en|access-date=2019-12-12}}</ref><ref>{{Cite web|url=https://www.thefreedictionary.com/Singularity+(mathematics)|title=Singularity (mathematics)|website=TheFreeDictionary.com|access-date=2019-12-12}}</ref>

 

 

has a singularity at <math>x = 0</math>, where it seems to "explode" to <math>\pm\infty</math> and is hence not defined. The absolute value function <math>g(x) = |x|</math> also has a singularity at , since it is not differentiable there.

has a singularity at <math>x = 0</math>, where it seems to "explode" to <math>\pm\infty</math> and is hence not defined. The absolute value function <math>g(x) = |x|</math> also has a singularity at , since it is not differentiable there.

在x=0处有一个<font color="#ff8000">奇点</font>，在这里它似乎“爆炸”到±∞，因此没有定义。绝对值函数g（x）=| x |在x=0处也有<font color="#ff8000">奇点</font>，因为它在那里不可微。

在x=0处有一个<font color="#ff8000">奇点</font>，在这里它似乎“爆炸”到±∞，因此没有定义。绝对值函数g（x）=| x |在x=0处也有<font color="#ff8000">奇点</font>，因为它在那里不可微。<ref>{{cite book |first=Geoffrey C. |last=Berresford |first2=Andrew M. |last2=Rockett |title=Applied Calculus |location= |publisher=Cengage Learning |year=2015 |isbn= 978-1-305-46505-3|page=151 |url=https://books.google.com/books?id=wzNBBAAAQBAJ&pg=PA151 }}</ref>