# 开源的Ruby项目

1. 停止理论化。
2. 写很多软件。
3. 从错误中学习。

......我有兴趣在帮助开源社区的过程中提高自己的技能，所以我想问问任何人是否有任何关于您熟悉或参与的用Ruby编写的有趣/有趣的开源项目的建议。

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## 13 答案

- 找出序列的组合定义，并且当你稍微延伸时，看看它是否有意义。

- 如果你正在尝试执行一个真空任务（例如平铺一个空白板或计算在空集上定义的函数），你可以用一种方法完成。你的大多数例子属于这个类，包括一个^ 0（在空集上定义的函数），0！ （空集上的双射），F_1（平铺空板）以及没有组的直接产品的基数（从每个类中选择一个对象，因此直接产品应该是标识）。

- 空数等于0，空产品等于1.（再次，0组的直积的基数应为1）。

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Poonen声称，我同意，0x0矩阵的行列式应该等于1.考虑当你试图扩大未成年人1x1矩阵的行列式时会发生什么。

Here's the standard example of a sequence that extends to zero in different ways: the sequence that is identically zero on the positive integers. One extension is the zero function. Other extensions interpret the sequence as n -> k 0n for some nonzero k.

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@LSpice我写这篇文章已经快六年了，但我认为我的意思是说较高的同伦群需要指向空格作为输入，所以如果你想通过自然扩展$\ pi_n的定义来定义$ \ pi_0  for $n> 0$，你应该有一个尖锐的空间作为输入。你当然可以自由定义$\ pi_0$，只要你喜欢。

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Also, 0! = Γ(1) = int_0^\infty e^(-t) = 1 ; here there's nothing special about 0. (But Γ isn't defined for nonpositive integers.)

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For a pointed space (X,p), the nth homotopy group πn(X,p) is usually defined as the group of maps of the n-sphere which take (1,0,...,0) to p, modulo homotopy-rel-basepoint. What's potentially weird is that S0 is disconnected, whereas Sn is connected for n>0. But then π0(X) just counts the number of path components of X. Of course, it doesn't have a group structure because S0 isn't a cube with its boundary identified; this is anomalous.

On the other hand, this corresponds perfectly with the other characterization of homotopy groups I've seen, where π0(X,p) is defined to be the set of path components of X, and then πn(X,p) is inductively defined as the "loop space" of πn-1(X,p), i.e. the group of homotopy classes of loops starting and ending at the basepoint (rel basepoint, of course), with composition defined simply as composition of loops.

So, while in neither setup is π0(X,p) a group, I think this is as well-defined as it's going to get. As far as I know, only in the setting of Lie groups is there a natural way to put a group structure on the path components (just take G/G0, where G is the Lie group and G0 is the path component of the identity).

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Rubyforge 上的活动项目是一个很好的开始。什么是一个好的入门项目是挑一个非常受欢迎但不是很多开发者的项目。

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