20240430230052-addition.org

Addition

Addition is the arithmetic hyperoperation where $n=1$. Addition is the repetition of the successor function.

Components

Parity

addition requires two operands to return a value.

operands

augend

for $a$ and $b$, such that $a + b = c$

$a$ is called the augend in the strict sense.

addend

for $a$ and $b$, such that $a + b = c$

both $a$ and $b$ are called addends in the broad sense.

$b$ is called the addend in the strict sense.

values

sum

for $c$, such that $a + b = c$

$c$ is called the sum.

Mathematical Implementations ** subtraction

subtraction is the inverse operation of addition. subtraction can also be represented as the addition of the roam:additive inverse of the subtrahend.

multiplication

multiplication is repeated addition.

summation

summation is addition extended to a sequence of numbers. summation represents a discrete series. it is usually denoted with capital Σ.

roam:integration

integration is the continuous extension of addition. it is the $lim_x→\infty$ of

Properties of addition

Commutativity

Associativity

Distributivity

Identity element

Applications