The Transitive Property
Published June 7, 2012 | 
Here’s a simple and nifty mathematical property that’s great to use in lessons for beginners, and also just plain useful for everyone else. It’s called the ‘transitive property,’ which states that:
If there exists some number a such that a=b,
and b=c,
then a=b=c, or a=c.
You see? It might be simpler to think of the variables a, b, c as terms to make things clearer, so if we were to say:
3=(1+2)
and (1+2)=(1+1+1),
then obviously 3=(1+1+1).
This also works for inequalities, where
if a>b, and b>c, then a>b>c, or a>c.
Let’s use concrete numbers again as an example:
If 3>2, and 2>1, then 3>1.
Pretty straightforward, right? And yet it’s a vital building block for much of mathematics. Learning and internalizing the transitive property is the first step towards a more complete understanding of algebra and other forms of higher math. If you’re instructing younger students, it’s essential to make sure they understand this concept!
