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Comment by _Donny | Hacker News Reader

I think this is spot on, at least for me personally.

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 = 0

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There is this phrase, often used when describing the decimal expansion of pi - "keeps going infinitely". This phrase is not exactly incorrect, but I wonder if it misleads people into thinking that an "infinite decimal" is "a kind of infinity", which it really isn't in any meaningful way.

I think it absolutely gets confused.

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).

That causes a contradiction which is why infinity can't be used that way. But what is the contradiction with 0.999... = 1?

Multiply both sides by ‘x’, then subtract one side from the other, then take the limit as x -> inf. This is obviously undefined. To get to zero, you have to make a new rule that one form of infinity is bigger than another form of infinity.

Infinity is very slippery, and there are several divergent fields of math that depend on particular definitions of it.

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