For mig giver det dog slet ikke mening, at man vil bevise 0,999… = 3/3 = 1 ved at starte med 0,333… = 1/3. Jeg vil dog hellere se “beviset for at man kan starte med det som udgangspunkt for sin bevisførelse… som jeg læser dit wiki link, så er det også der “magien” sker:

But the proofs shed little light on the fundamental relationship between decimals and the numbers they represent, which underlies the question of how two different decimals can be said to be equal at all.[1] William Byers argues that a student who agrees that 0.999… = 1 because of the above proofs, but hasn’t resolved the ambiguity, doesn’t really understand the equation.[2] Fred Richman argues that the first argument “gets its force from the fact that most people have been conditioned to accept the first line without thinking”.[3]

Once a representation scheme is defined, it can be used to justify the rules of decimal arithmetic used in the above proofs. Moreover, one can directly demonstrate that the decimals 0.999… and 1.000… both represent the same real number, it is built into the definition. This is done below

Så jeg stiller spørgsmålet retur – hvilken type er du?