 Addition

Addition combines two numbers into their sum. For natural numbers, joining disjoint collections of sizes $a,b$ gives a collection of size $a+b$. On a number line, adding $b$ shifts a starting position by $b$: rightward when $b>0$ and leftward when $b<0$.

Starting at $2$ and adding $3$ reaches $5$. Starting there and adding $-3$ returns to $2$, because $3+(-3)=0$. Additive inverses turn this return move into an algebraic rule. With real numbers, addition is commutative and associative: exchanging two shifts or grouping several shifts differently leaves the final position unchanged.

The bottom panel applies $x\mapsto -3x/2$. Input $2$ becomes $-3$, and input $-2$ becomes $3$. Multiplication by a negative real number rescales distances from zero and reverses direction, giving a reflection in mathematics as well as a scale change. This is a different operation from shifting every input by one fixed amount.

Addition is a fundamental mathematical operation that involves combining two or more numbers to obtain a total or sum. It is one of the four basic arithmetic operations, alongside subtraction, multiplication, and division. The symbol used for addition is "+". For example, in the expression \(3 + 2\), the numbers 3 and 2 are added together to yield a result of 5.