Transitivity Definition

Transitivity

1. logic mathematics (of a relation) such that, if it applies between successive members of a sequence, it must also apply between any two members taken in order. For instance, if A is larger than B, and B is larger than C, then A is larger than C.

Basically if one thing is or isn’t equal to one thing, it still would be equal or not equal to that thing no matter where you place it in the equation.

Transitivity for Equality: For any real numbers $a$, $b$, and $c$, if $a=b$ and $b=c$, then $a=c$. Transitivity for Inequality: For every a, b, and c in R, if $a<b$ and $b<c$ then $a<c$. Basically, $a<b<c$.