Problem regarding a MST proof of 0.99999\cdots=1

Kaiya Hardin

Kaiya Hardin

Answered question

2022-04-23

Problem regarding a MST proof of 0.99999=1

Answer & Explanation

kubistiedt

kubistiedt

Beginner2022-04-24Added 17 answers

Step 1
There is a problem with this proof, but it's not where you're looking for it. Its logic is supposed to be: assume both numbers are different, then, there must be a number strictly between them ("...between two distinct real numbers, there's always another one..."), and that leads to a contradiction. The way the contradiction is reached is faulty, though: "The decimal representation of x must have ..." is implicitly assuming that there is a unique decimal representation of x, while proving that
0.9999=1.0000
i.e. that decimal representation is not always unique. A proof proving its own invalidity is a rare specimen.

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