Talk:De Bruijn index

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Mathematics rating:
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Field:  Foundations, logic, and set theory

Core "Formal definition" section has to be rewritten

Acoording to current version:

(λ λ 4 2 (λ 1 3)) (λ 5 1) = λ 3 (λ 6 1) (λ 1 (λ 7 1))

(λx. λy. z x (λu. u x)) (λx. w x) = (λy. z (λx. w x) (λu. u (λx. w x)))

but (λy. z (λx. w x) (λu. u (λx. w x))) could not be written as λ 3 (λ 6 1) (λ 1 (λ 7 1)), but as λ 3 (λ 6 1) (λ 1 (λ 6 1))

• Term "ith free variable" is unclear but crucial to understanding of substitution process.
• Same for M[1.1[s'].s[s'].3[s']...]. —Preceding unsigned comment added by 46.146.233.123 (talk) 15:30, 30 January 2011 (UTC)
I think you're mistaken. Here's some ASCII art to help you out:
```      ,-----+  ,---+   ,-+  ,---+
λ λ λ λ λ λ 3 (λ 6 1) (λ 1 (λ 7 1))
\____________/____________/
```
20:50, 31 January 2011 (UTC)

Improper template, but more--improper capitalization throughout article as well

De Bruijn should always have an initial capital D when it starts a sentence, just like anything else. We don't capitalize copper all the time, but we do when it starts a sentence. And our Wikipedia article is at "Copper", with no "lowercase" template. We don't capitalize the newton all the time, but we do when it starts a sentence. And our Wikipedia article is at "Newton", with no "lowercase" template. We don't capitalize "heat index", but our article is at Heat index, with no "lowercase" template.

And it is so used at the start of a sentence in this article. That alone is enough to make the lowercase template inappropriate for this article.

But in this case it is also much more than that. De Bruin should start with a D when it starts a sentence, but also it should be De Bruin with a capital D any time this surname is not preceded by a given name or a title.

See, for example, United States Government Printing Office Style Manual, Chapter 3, Capitalization rules:[1]

• 3.13. In foreign names such particles as d', da, de, della, den, du, van, and von are capitalized unless preceded by a forename or title. Individual usage, if ascertainable, should be followed.
Da Ponte; Cardinal da Ponte
Den Uyl; Johannes den Uyl; Prime Minister den Uyl
Du Pont; E.I. du Pont de Nemours & Co.
Van Rensselaer; Stephen van Rensselaer
Von Braun; Wernher von Braun
but d'Orbigny; Alcide d'Orbigny; de la Madrid; Miguel de la Madrid

Gene Nygaard (talk) 05:08, 21 December 2008 (UTC)

Need further explanation of M[1.1[s'].s[s'].3[s']...]

Could someone please explain what the notation in the subject, which was copied from the article right after:

``` The rules for the application are as follows:
```

means?

Thanks very much.

Cppljevans (talk) 19:18, 3 October 2010 (UTC)