Abstract
In this note, we discuss two specific cognitive biases towards closure property as a learning obstacle in school mathematics in the context of number sets. These biases are related to rational and irrational numbers, two important and challenging issues from an educational point of view. The first bias concerns incorrect application of rules and properties of closure property in rational numbers to irrational numbers, and the second deals with the improper generalisation of the closure property in finite states to infinite states. These biases indicate the importance of teaching and learning the closure property.
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