### Abstract

Every element u of [0, 1] can be written in the form u = x^{2}y, where x, y are elements of the Cantor set C. In particular, every real number between zero and one is the product of three elements of the Cantor set. On the other hand, the set of real numbers v that can be written in the form v = xy with x and y in C is a closed subset of [0, 1] with Lebesgue measure strictly between 17/21 and 8/9. We also describe the structure of the quotient of C by itself, that is, the image of C × (C \ {0}) under the function f (x, y) = x/y.

Original language | English (US) |
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Pages (from-to) | 4-17 |

Number of pages | 14 |

Journal | American Mathematical Monthly |

Volume | 126 |

Issue number | 1 |

DOIs | |

State | Published - Jan 2 2019 |

### Keywords

- MSC: Primary 28A80
- Secondary 11K55

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Athreya, J., Reznick, B., & Tyson, J. T. (2019). Cantor Set Arithmetic.

*American Mathematical Monthly*,*126*(1), 4-17. https://doi.org/10.1080/00029890.2019.1528121