Slightly off topic to the main point of the article, which is how to deal with not understanding something.
For anyone who wants to fully understand this, you need to read “Baby Rudin”: Rudin “Principles of Mathematical Analysis”.
Real numbers are defined as equivalence classes of convergent series. The series 1,1,1,1,1 and 0.9, 0.999 … are in the same equivalence class and so are the same real number. People often get caught up with the assumption that two different series (or two different decimal representations) must be different numbers.
Slightly off topic to the main point of the article, which is how to deal with not understanding something.
For anyone who wants to fully understand this, you need to read “Baby Rudin”: Rudin “Principles of Mathematical Analysis”.
Real numbers are defined as equivalence classes of convergent series. The series 1,1,1,1,1 and 0.9, 0.999 … are in the same equivalence class and so are the same real number. People often get caught up with the assumption that two different series (or two different decimal representations) must be different numbers.
If you study a bit more, though, it stops being necessarily true; https://arxiv.org/abs/1307.7392
Yes; Ignorance is followed by enlightenment which is followed by the fog of war.