A note on the definitions of the functions NQ, NR, and NL, which account for our concepts of numerical quantity, numerical rank, and numerical label, respectively:

In what follows, I introduce an ontology for our conceptualisation of number contexts that is grounded in the representation of numerical tools. In order to keep things simple, I focus on counting sequences as our primary numerical tools. However, according to our criteria-based approach there are also other progressions that can serve as numerical tools. When we acquire these progressions, their representation is integrated into our concept of ‘number sequence’.

The definitions are hence generalised in order to cover all sequences that are introduced as number sequences: instead of ‘counting sequence’ I use the general term ‘numerical sequence’ for any sequence that fulfils the number criteria and is conventionally used as a set of numerical tools (where the above-defined sequence C is one instance for such a sequence).

As shown in chapter 7 non-verbal numerals can also play this role. In this case, the final argument of NQ, NR, and NL, respectively (the argument identified as ‘ɑ’ in the definitions) is not an element of a counting sequence C, but for instance an element of the sequence A of arabic numerals whose initial element in these mappings is then the element corresponding to ‘one’, namely ‘1’.