- Rational Numbers :
- Numbers that can be represented/written in the form p / q where p and q are integers and q is not 0
- Any integer or whole number can also be written in the format p/q. e.g. 4 can be written as 8/2 or 4/1 or 12/3 … Similarly, -5 can be written as 10/-2 or -25/5 or -5/1 …
- The Sum of two rational numbers is a rational number which means “Rational Numbers are closed under addition”
- The Difference between two rational numbers is a rational number which means “Rational Numbers are closed under subtraction”
- The product of two rational numbers is a rational number which means “Rational Numbers are closed under division”
- The division of two rational numbers is not a rational number which means “Rational Numbers are NOT closed under division”. This is primarily because for a rational number a, a / 0 is not defined.
| Numbers | ||||
| Addition | Subtraction | Multiplication | Division | |
| Rational Numbers | Yes | Yes | No | |
| Integers | Yes | No | ||
| Whole Numbers | Yes | |||
| Natural Numbers | No |
$latex i\hbar\frac{\partial}{\partial t}\left|\Psi(t)\right>=H\left|\Psi(t)\right>$