this post was submitted on 27 Jun 2024
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Let me restate: I am of the opinion that repeating decimals are imperfect representations of the values we use them to represent. This imperfection only matters in the case of 0.999... , but I still consider it a flaw.
I am also of the opinion that focusing on this flaw rather than the incorrectness of the person using it is a better method of teaching.
I accept that 1/3 is exactly equal to the value typically represented by 0.333... , however I do not agree that 0.333... is a perfect representation of that value. That is what I mean by 1/3 ≠ 0.333... , that repeating decimal is not exactly equal to that value.