**Transitivity **

The mathematical relationship ‘is a multiple of’ applied to numbers possesses what is called the transitive property. This means that if A is a multiple of B and B is a multiple of C then it follows that A is a multiple of C. This is illustrated in general terms in the figure below.

**How does transitivity apply to measurement?**

The principle of transitivity is shown in the diagram above. If we know that A is related to B (indicated by an arrow) and B is related to C, the question is whether A is related to C as a logical consequence. With some relations (such as ‘is a factor of’) it does follow logically and we can draw in the arrow connecting A to C. .

We can now see that whenever we compare and order three or more objects (or events) using a measuring attribute such as their lengths, their masses, their capacities or the length of time (for events), then we are again making use of a transitive relationship.

The transitive property of measurement can be expressed formally using inequality signs as follows:

If A < B and B < C then A < C.