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The construction of a numerical sequence requires an ordinal model of conceptual support that can be defined by the given relationships in a system of progressions. Taking into account the ordinal model of conceptual support leads us to a coherent conceptual/interpretative system which takes into consideration conceptions and beliefs regarding numerical sequencing that immediately takes us back to epistemological and didactic considerations. Epistemological approaches are confined to looking at the nature, origin and mode of existence of the natural number and elementary arithmetic, so that construction of the numerical sequence relies, at this point, on the conclusions that are drawn in regard to the said problem. [ABSTRACT FROM AUTHOR]