0.999… repeating (or 0.9‾0.\bar{9}) is equal to 1. It’s a fact. To some, this is highly counterintuitive, unbelievable even. I’ve seen various explanations for how it works, from informal explanations to formal proofs. I recently found an interesting (not original) proof, but first I’ll give a couple less rigorous explanations. Informal arguments Tripling a third…
Tag: notation
Stories of math notation (part 2): The worst notation in mathematics
Sometimes notation is confusing. One way this can happen is when the same notation is used for multiple different concepts. Usually, if the same notation is used for different things, they occur in different contexts which allows them to be distinguished. In at least one case, the same notation is used for different things in…
Stories of math notation (part 1): y should come before x
Or rather, perhaps both the symbols and positions for x and y should be switched. The convention of writing coordinates as (x, y) is so deeply ingrained that, in my opinion, it causes confusion in situations where x doesn’t naturally come first. Reasons for x first As I see it, the primary reason for writing…
thoughts on mind 