Recently, after work beers with a colleague went down a bit of rabbit hole as he attempted to "red pill" me on a couple of topics. One of those happen to relate to the below self-published paper, which was written by someone he went to college with: https://www.slideshare.net/MrIndererminate/indeterminate-is-not-synonymous-with-undefined It seems rather compelling on first read, but acknowledging that it is above my paygrade, I decided to search the internet to see if counter arguments had been made, which led me to a thread on this forum, where the paper had been mentioned: https://www.physicsforums.com/threads/graphing-a-strange-equation.912296/ To ensure I can convey the pro-hole argument effectively, I'm just going to lay out my simple version of it below: Equality A [ y = (x^2-1)/(x-1) ] cannot be rearranged into Equality B [ y (x-1)=(x^2-1) ] ,as this would involve division by zero. It is true that graphing B on a cartesian plane will result in a vertical line. However, this does not mean that a vertical line should be depicted when graphing A, as it cannot be rearranged into B without fundamentally changing the equality. For A, when x=1 y=0/0. Thus hole at co-ordinate (1,2) is the appropriate depiction for A, as all division by zero is undefined. Is this correct? Are there any other points I should add?