# Closure (mathematics)

Sometimes, if one includes an element to make closure, it makes more changes. For example, if one includes infinity, ${\displaystyle \infty =1/0}$, that is closure of division, the laws of addition and subtraction are changed. There is no inversion of addition for ${\displaystyle \infty }$.
• ${\displaystyle B=A_{0}\cap A_{1}}$
• ${\displaystyle C={\cup _{n}}A_{n}}$