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| Main Authors: | , |
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| Format: | Preprint |
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2026
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| Online Access: | https://arxiv.org/abs/2604.04647 |
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| _version_ | 1866910105768820736 |
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| author | Bergstra, Jan A Tucker, John V |
| author_facet | Bergstra, Jan A Tucker, John V |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_04647 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On Ambiguity: The case of fraction, its meanings and roles Bergstra, Jan A Tucker, John V Logic in Computer Science Computation and Language Symbolic Computation 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. |
| title | On Ambiguity: The case of fraction, its meanings and roles |
| topic | Logic in Computer Science Computation and Language Symbolic Computation |
| url | https://arxiv.org/abs/2604.04647 |