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I just cited myself.
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this post was submitted on 27 Jun 2024
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I'm not saying that math works differently is different bases, I'm using different bases exactly because the values don't change. Using different bases restates the equation without using repeating decimals, thus sidestepping the flaw altogether.
My whole point here is that the decimal system is flawed. It's still useful, but trying to claim it is perfect leads to a conflict with reality. All models are wrong, but some are useful.
you said 1/3 ≠ 0.333... which is false. it is exactly equal. there's no flaw; it's a restriction in notation that is not unique to the decimal system. there's no "conflict with reality", whatever that means. this just sounds like not being able to wrap your head around the concept. but that doesn't make it a flaw.
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.