Jul 22, 2017 · 1 min read
“ You know that two different numbers, should in fact be different numbers.”
Two different numbers ARE different numbers. 0.9(9) and 1 are two different representations of the same number.
There are many more cases: 1/2 = 2/4 = 3/6, for instance. 5¹ = 5. 1/sqrt(2) = sqrt(2)/2. Every number has an infinite number of different representations, so it shouldn’t be surprising that 1 can be represented multiple ways, including 0.9(9) and -e^(i pi) and i⁴.
If this is understood, there’s nothing counterintuitive about 0.9(9) = 1. The problem is that we allow for the intuition that different representations must be different numbers.
