User blog comment:Vel!/1+w/@comment-5982810-20141011211100/@comment-5982810-20141011213352

" In the comment above you said that you never claimed 1+w != w, and I've just given a quote in which you  do  claim that they are distinct in your considerations." --LP

Yeah the key word is "treat", as in we can treat them in this manner. They can be thought of as distinct indexes leading to distinct functions. Nowhere in the article do you find equalities like 1+w!=w or w!=1+w, because it's not relevant. It be like asking what #*#^# equals. It's just an expression, it doesn't have a value. However #*#^#[n] = #^#[n+1] is still perfectly valid. We can assume two expressions are equal, if and only if they are identical. If they are different then an equality must be demonstrated. But there is no way to prove #*#^# = #^# in ExE nor is there a way to prove 1+w = w with my FGH variant.