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$latex 1+3=7$,  $latex 2+4=10$, $latex -7+3=-1$ and so on. From the three additions people might have concluded that in general, for any integers $latex x$ and $latex y$ we have $latex x+y=x+y+y$ which is again integer. But the last writing of course could be misleading as on the both side we use symbol $latex +$ to represent two different things. The left one is not usual $latex +$ while the right one represents usual $latex +$. To counter this problem, instead using $latex +$ in the left hand side,  we can change the $latex +$, for instance by $latex *$. Therefore $latex x*y$ is meant for $latex x*y=x+y+y$. Hence we have $latex 1+2=5$ and so on. The definition is also possibly alternated as long as the result is again in the domain we state in the beginning, as in the example above is the set of all integers.