A function $latex f:A \rightarrow B$ is called injective function (or one one function) if for any $latex x,y\in A$ it follows that $latex f(x)=f(y)$ implies $latex x=y$.

Other than the above definition, there are several equivalent definitions. Here they are.

The first one is of course the contraposition of the previous one.

A function $latex f:A \rightarrow B$ is called injective function (or one one function) if for any $latex x,y\in A$ it follows that $latex x\neq y$ implies $latex f(x)\neq f(y)$.

The second one is: Continue reading →

It is common that people that are not getting along with math in their daily life, always think $latex 1+2=3$, $latex 5+3=8$ etc. as addition we use in daily life is an unadorned addition as what people understand. But mathematically, it is possible  for us to define other additions differ from the unadorned one. For instance, let us collect all integers and let us define on the set, an addition defined by Continue reading →