We contemplate the notion of ambiguity in mathematical discourse. We consider a general method of resolving ambiguity and semantic options for sustaining a resolution. The general discussion is applied to the case of `fraction' which is ill-defined and ambiguous in the literature of elementary arithmetic. In order to clarify the use of `fraction' we introduce several new terms to designate some of its possible meanings. For example, to distinguish structural aspects we use `fracterm', to distinguish purely numerical aspects `fracvalue' and, to distinguish purely textual aspects `fracsign' and `fracsign occurence'. These interpretations can resolve ambiguity, and we discuss the resolution by using such precise notions in fragments of arithmetical discourse. We propose that fraction does not qualify as a mathematical concept but that the term functions as a collective for several concepts, which we simply call a `category'. This analysis of fraction leads us to consider the notion of number in relation to fracvalue. We introduce a way of specifying number systems, and compare the analytical concepts with those of structuralism.

翻译：本文探讨数学论述中的模糊性概念。我们考虑了一种通用的模糊性消解方法，以及维持消解结果的语义选择。这一通用讨论被应用于“分数”这一在初等算术文献中定义不清且存在歧义的概念。为澄清“分数”的用法，我们引入了若干新术语来指代其可能的含义。例如，为区分结构方面，我们使用“分式项”（fracterm）；为区分纯数值方面，使用“分值”（fracvalue）；为区分纯文本方面，则使用“分号”（fracsign）和“分号出现”（fracsign occurrence）。这些阐释可消解模糊性，我们讨论了在算术论述片段中通过使用此类精确概念进行消解的过程。我们提出，分数并非一个合格的数学概念，而是作为多个概念的统称，我们将其称为“范畴”（category）。对分数的这一分析促使我们思考数值与分值之间的关系。我们引入了一种指定数系的方法，并将这些分析概念与结构主义的概念进行了比较。