Decimal representations are not unique. Every number that terminates with an infinite string of zeros can be represented by an expression that terminates with an infinite string of 9's. To understand this further, you would need to learn some topology and/or analysis. The equality comes from something called the -principle. Given two numbers , if for all , , then . Here, is the absolute value function, so I am referring to real numbers. If you are using a different metric , then if for all , you have .