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Nonsymbolic and symbolic representations of null numerosity
Rut Zaks-Ohayon1, Michal Pinhas2, Joseph Tzelgov3,4,5
1Department of Cognitive and Brain Sciences, Ben-Gurion University of the Negev, 84105, Beer Sheva, Israel. zaksru@post.bgu.ac.il.
Psychological Research
|April 12, 2021
Summary
Perceiving the empty set as a number depends on notation consistency and task type. Zero (0) is consistently treated as a number, unlike the empty set.
Area of Science:
- Cognitive Psychology
- Numerical Cognition
Background:
- Null numerosity, including the empty set and zero (0), can be processed numerically.
- Understanding the conditions for representing null numerosity as a numerical entity is crucial.
Purpose of the Study:
- To investigate the conditions under which nonsymbolic (empty set) and symbolic (0) null numerosity are perceived as numerical entities.
- To examine the influence of notation homogeneity and task demands on the processing of null numerosity.
Main Methods:
- Utilized magnitude comparison and same/different numerosity judgment tasks.
- Employed distance and end effects as measures of numerical processing.
- Tested notation homogeneous (nonsymbolic-nonsymbolic, symbolic-symbolic) and heterogeneous (nonsymbolic-symbolic) pairs.
Main Results:
- Comparisons involving zero (0) showed faster responses and reduced distance effects across all conditions.
- Comparisons involving the empty set showed these effects only in notation homogeneous conditions.
- A distance effect for 'different' judgments emerged for 0 but not the empty set when paired with digits.
Conclusions:
- The perception of the empty set as a numerical entity is contingent on notation homogeneity and specific task requirements.
- Zero (0) is consistently processed as a numerical entity, irrespective of notation or task.
- These findings highlight the distinct cognitive representations of the empty set versus zero.
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