Integer arithmetic
= Integer arithmetic
Integer arithmetic computes with <integers>. <Addition>, <subtraction> and <multiplication> preserve <integer> values; <division> can instead return a <quotient> and <remainder> through <Euclidean division>. For example, $102=20\cdot5+2$ gives five complete groups and a remainder of two. The <ceiling count for fixed-size batches> requires six groups to hold all 102 items.
Mathematical <integers> have no fixed size bound. A computer representation may have one, so an exact arithmetic formula still requires sufficient space for its inputs and intermediate values. The <floor function> and <ceiling function> define mathematical bounds independently of a chosen representation.