Two notes on notation · HackerPapers discussions

Two notes on notation — HN submission

Wed, 24 Jun 2026 13:03:41 GMT

Two Notes on Notation (Knuth, 1992)

1 point; 0 discussion replies on HN. Paper and source history. A submission is not an endorsement.

Two notes on notation — HN submission

Sun, 07 Jun 2026 17:51:18 GMT

Two notes on notation (Knuth, 1992)

1 point; 0 discussion replies on HN. Paper and source history. A submission is not an endorsement.

Two notes on notation — mentioned by svat

Sat, 12 Jun 2021 00:31:35 GMT

Note that the abstract at https://arxiv.org/abs/math/9205211 is not by Knuth (it says "Abstract added by Greg Kuperberg" in small print). Anyway, the "two notes" of the title are about: 1. Iverson bracket notation: writing say "[x ≥ 5]" to mean "1 if x ≥ 5, and 0 otherwise" (casting the boolean condition to a 0–1 integer, in programming terms). He has good examples of how it seems unnecessary or innocuous at first (one starts out writing "1" for an indicator function, or putting it in subscripts), but as you do more and more manipulations of sums it grows on you and you realize how useful the…

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Two notes on notation — mentioned by threatofrain

Fri, 11 Jun 2021 22:45:38 GMT

Original link is broken. Use this one. https://arxiv.org/abs/math/9205211

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Two notes on notation — HN submission

Fri, 11 Jun 2021 21:57:52 GMT

Two notes on notation (1992)

18 points; 9 discussion replies on HN. Paper and source history. A submission is not an endorsement.

Two notes on notation — mentioned by tlb

Thu, 15 Apr 2021 21:35:41 GMT

Knuth [0] discusses in more detail some advantages of indicator notation, in particular that, when you eliminate the limits on summations, it makes it much easier to do algebra on summations. [0] https://arxiv.org/abs/math/9205211

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Two notes on notation — mentioned by dubya

Thu, 21 Nov 2019 15:11:07 GMT

I don't know if Knuth popularized it, but it's somewhat common in combinatorics. Similar idea to using indicator functions when doing change of variables in calculus. https://arxiv.org/abs/math/9205211

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Two notes on notation — mentioned by jacobolus

Wed, 23 Oct 2019 03:32:45 GMT

This seems almost exactly backwards to me. “Geometric” proofs (i.e. based on spatial reasoning) are fast and fluid, relying on an imagined spatial configuration which can be seen all at once. “Algebraic” proofs (i.e. based on symbol manipulation) are serialized and low-bandwidth, and working them out takes a significant amount of laborious fiddling with symbols on paper, and is almost impossible to work out mentally except in nearly trivial cases. The benefit of the “algebraic” version is often that putting in that labor can often yield a result even when the prover has no special insight.…

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Two notes on notation — HN submission

Thu, 27 Jun 2019 09:25:19 GMT

Donald E. Knuth: Two notes on notation (1992)

2 points; 0 discussion replies on HN. Paper and source history. A submission is not an endorsement.

Two notes on notation — mentioned by svat

Sun, 15 Oct 2017 17:30:30 GMT

My point was that the notation should be optimized for the people using it, not for the technology used to typeset it. If the notation is suboptimal for the people then it can definitely be changed, but that's a different reason. Note that some of these notational improvements may actually make it harder to typeset. For example, the second part of Knuth's paper "Two Notes on Notation" (https://arxiv.org/abs/math/9205211) introduced improved notation for the Stirling numbers "of the first kind" and "second kind", replacing easier-to-typeset but less informative notation like S(n,k). This…

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Two notes on notation — mentioned by evanb

Thu, 24 Aug 2017 15:18:47 GMT

Also along those lines: Two notes on notation, Knuth, https://arxiv.org/abs/math/9205211

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Two notes on notation — mentioned by dahart

Sat, 25 Jun 2016 23:03:44 GMT

This is a great example. Wikipedia has the same one with isolines demonstrating this point in the 0^0 subsection of the exponentiation article, here: https://en.m.wikipedia.org/wiki/Exponentiation#Continuous_ex... With the caveat: "However, under certain conditions, such as when f and g are both analytic functions and f is positive on the open interval (0, b) for some positive b, the limit approaching from the right is always 1.[26][27][28]" Also, definitely take note of Knuth's argument, because while you might feel strongly that indeterminate is the right answer right now, there are big…

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Two notes on notation — mentioned by joefkelley

Sat, 25 Jun 2016 19:04:12 GMT

Here's Knuth's opinion on 0^0: http://arxiv.org/pdf/math/9205211v1.pdf (on page 6) He makes a few pretty convincing points about why it's useful to define it equal to 1, while admitting that in some sense, it's not quite as well defined as say 0+0.

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Two notes on notation — mentioned by anderskaseorg

Sat, 11 Apr 2015 23:44:02 GMT

Defining 0^0 = 1 is just as important in analysis as it is in combinatorics, even though analysis texts aren’t always clear that they’re making use of this fact. • If p(x) = ∑[n=0..∞] a_n x^n is a power series, then p(0) = a_0 is its constant term, but it makes no sense to write this unless 0^0 = 1. • The power rule d/dx [x^n] = n x^(n−1) holds for n = 1 and x = 0, but this requires 0^0 = 1. The reason that some people believe it’s important to undefine 0^0 in analysis is that the limiting expression lim[x → a] f(x)^g(x) does not necessarily exist when lim[x → a] f(x) = lim[x → a] g(x) = 0.…

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Two notes on notation — mentioned by Sniffnoy

Thu, 03 Apr 2014 01:33:23 GMT

Why link to the PDF? Better to just link to the abstract: http://arxiv.org/abs/math/9205211 Edit: To be clear, this is good practice when linking to arXiv in general. From the abstract, one can easily click through to the PDF; not so the reverse. And the abstract allows one to do things like see different versions of the paper, search for other things by the same authors, etc.

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Two notes on notation — mentioned by yaks_hairbrush

Thu, 03 Apr 2014 00:57:58 GMT

A word from Knuth on the matter (warning: PDF): http://arxiv.org/pdf/math/9205211v1.pdf See page 6.

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Two notes on notation — mentioned by cma

Sat, 11 May 2013 17:07:14 GMT

It shouldn't be a subclass of int. http://arxiv.org/abs/math/9205211

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