And at the point where students see this, the whole concept of real numbers and infinity is usually ill-defined. I actually understand the scepsis for this theorem and where it comes from. The proof relies on the existence of a supremum, which is non-trivial.
I am not very good at mathematics, so I never questioned my professors when they said that "You cannot treat infinites as regular numbers".
Perhaps due to that statement, I did not really pursue these kinds of equations. For instance, I do not really see how the algebraic argument on the Wiki is any different from:
2 * inf = inf
inf + inf = inf (subtract inf from both sides)
inf = 0Infinity is very slippery, and there are several divergent fields of math that depend on particular definitions of it.
Infinity, the number, is routinely confused with creating an onto function mapping digits of pi to a set with a cardinality of the natural numbers. But sadly most people don't have the mathematical maturity to understand the difference when they encounter their first irrational number (normally pi).