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<p>Equating 0.999… (infinitely repeating nines after the decimal point) with 1 has provoked bewilderment, as well as various justifications, discussions and research engagements. The equality can also be seen as an example of a more general mathematical phenomenon, which begs the question, what does it exemplify? We introduce a theoretical construct “space of an example,” as a variation on the notion of “example spaces,” and explore how prospective secondary school teachers situate this particular equality within a broader mathematical space. Responding to the question “of what is this an example?” participants’ highlighted ideas related to (i) different representations of numbers, (ii) infinity, and (iii) approximation and limits. We argue that the “space of an example” is a useful research tool to uncover ideas related to a&#xa0;particular concept.</p>

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The equality 0.999… = 1, what does it exemplify? Exploring spaces of an example

  • 期刊论文

  • 发表日期：

    2025年12月11日

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  • Rina Zazkis,
  • Ami Mamolo

摘要

Equating 0.999… (infinitely repeating nines after the decimal point) with 1 has provoked bewilderment, as well as various justifications, discussions and research engagements. The equality can also be seen as an example of a more general mathematical phenomenon, which begs the question, what does it exemplify? We introduce a theoretical construct “space of an example,” as a variation on the notion of “example spaces,” and explore how prospective secondary school teachers situate this particular equality within a broader mathematical space. Responding to the question “of what is this an example?” participants’ highlighted ideas related to (i) different representations of numbers, (ii) infinity, and (iii) approximation and limits. We argue that the “space of an example” is a useful research tool to uncover ideas related to a particular concept.