Superficially, the fictitious element doesn't scale well to multidimensional arrays. Indexing multidimensional arrays from zero makes a naive (contiguous) conversion to a linear address space (systematically varying one index after the other) look simpler than when indexing from one. For instance, when mapping the three-dimensional array to a linear array L["M⋅N⋅P"], both with "M⋅N⋅P" elements, the index "r" in the linear array to access a specific element with in zero-based indexing, i.e. ≤ "x" < "P", ≤ "y" < "N", ≤ "z" < "M", and ≤ "r" < "M⋅N⋅P", is calculated by . Organizing all arrays with 1-based indices (≤ "x′" ≤ "P", ≤ "y′" ≤ "N", ≤ "z′" ≤ "M", ≤ "r′" ≤ "M⋅N⋅P"), and assuming an analogous arrangement of the elements, gives to access the same element, which arguably looks more complicated. Of course, since and A simple and everyday life example is positional notation which the invention of the zero made possible. In positional notation, tens, hundreds, thousands and all other digits start with zero, only units start at one.