The Weirdness in Maths

Posted on

I find it quite bizarre that there are a lot of mysteries and confusions and “weirdness” in the many wonders of mathematics. One example would be the fact that 0.999… = 1. This means that the number 0.9, followed by an infinite number of 9s, are all equal to 1. But not in the sense that this number is rounded up to 1. It is just equal to 1. But how could that be? We have all learned from middle school that the comparison of decimals involves comparing the integral part first before comparing the decimal part. And in doing so, the greater whole number, the greater its value; and then comparing the decimal part digit after digit after the decimal point. But in this case it seems that 0.999… is of a smaller value since its whole number value is 0 and 1 has an integral part of 1; this meant that 1 would have been greater number. But it seems that there exists a proof that proves that they are indeed both equal:

Let x = 0.999… Therefore, 10x = 9.999… (Multiplying by 10 means that you have to move the decimal point one place to the right). Also if you subtract these two numbers, we have (10x-x) = (9.999…-0.999…). Simplifying it, we have 9x = 9. (The decimal portion of both are both identical; hence they cancel out). Dividing both sides by 9, x = 1. And by transitive property, if x = 0.999… and x = 1, then it must be that 0.999… = 1.

Q.E.D.