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Erdős writing like a programmer

Here is a neat example of famous mathematician Pál Erdős (often rendered in English as Paul Erdős) writing like a programmer in 1961. He goes to some trouble to introduce notation that allows him to index everything from zero.

From “Intersection Theorems for Systems of Finite Sets” P. Erdős, Chao Ko, R. Rado; Quart. J. Math., Oxford (2), 12 (1961), pp. 313-320:


Now it isn’t too unusual for a mathematician to use half-open notation such as [0,5) to denote the real numbers greater than equal to zero and strictly less than five. But Erdős is using it to denote the set of integers {0, 1, 2, 3, 4} (pretty much exactly has Python’s function range(0,5) does).

The [0,5) notation isn’t too unusual, but Erdős goes much further:

  • He declares his intent to write [k,l) as {k,k+1,..., l̂} (instead of {k,k+1,..., l-1}.
  • He is indexing from zero quite often (even in subscripts, unusual for a mathematician).
  • In addition to writing out of bound indexes as he goes on (in the “set of all systems section”) to write unused sets as â_n where in addition to not using the set a_n in his collection, it could also be the case that n is an out of range index and there is not even any set a_n to skip!

Categories: Computer Science Mathematics

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Data Scientist and trainer at Win Vector LLC. One of the authors of Practical Data Science with R.

2 replies

  1. “Apologies for my limited fonts: using an umlaut instead of a double-acute and not being able to place caret on top of all symbols.”

    It is written as ” Pál Erdős ” properly
    (feel free to copy-paste it and update the post)

    1. Thanks, erosb.

      That motivated me to switch to Unicode (so I am hopefully less font-dependent) and clean up the notation a bit.