3. Sorts

Step Three of Learn to Count in Twelve Easy Steps

Reminder Step 2:

We have introduced the collection of additions we shall use. We have generated the aspects {a,b,c,k,u,t,q,s,w} of the 136 smallest pairs of a,b.

Step 3:

Today we introduce the concepts of order, sorting sequence, alpha, beta, gamma and delta.

Reason why:

We demonstrate that sorting of the data set creates a place for each addition. We show that using different sorting aspects may bring forth different sorting sequences, thus different places for the individual additions.

Action:

We begin by sorting the data set on arguments a and b. First, we generate the sorting order wherein a is the first, and b is the second sorting argument. This order we call SQ_ab. Please see column called SQ_ab in Table 3.num. here

Then, we generate the sorting order wherein b is the first, and a is the second sorting argument. This order we call SQ_ba. Please see column called SQ_ba in Table 3.num. here.

Discussion:

Method of definition:

We call that procedure a ‘sort,’ which results in the sequential numbers 1…136 being assigned to the additions in columns a…w, as visible there.

Further research can make the Twelve Easy Steps into Twelve Complicated Steps by using a non-deictic definition of the term ‘sort.’ Presently, we use the deictic method of definition.

Concepts:

The concept underlying the sort is that of an order. We see that the order as expressed by SQ_ab is different to the order as expressed by SQ_ba. The abstract idea, the concept of ‘order’ in both cases is identical.

We see that the set can be in two different, conflicting states of order. In dependence of the order, the place of an individual addition may be different. (Example: ordering a class of children once alphabetically on their names, once by their height, chances are that an individual child will come to a different place in the new sequence.)

We use the terms αβ and γδ to designate any one (in case of using αβ) or any two (in case of using αβ and γδ) of the sorting sequences, that is, any of the realisations of the order concept. α ≠ β, γ≠ δ.