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A comment on The Most Common Errors in Undergraduate Mathematics (2009). Parent comment

Re:The Most Common Errors in Undergraduate Mathematics (2009) by 6gvONxR4sf7o on Thursday November 19, 2020 @12:09PM (#25151618)
Nobody’s saying it’s totally invalid. I think you’re reading that into what they’re saying and you’re talking past each other.

The complaint is that students work backwards without understanding why working backwards is different than working forwards. So if they happen to do it correctly (e.g. by using reversible steps), then it’s only success via accident.

Done correctly, and on purpose, with the different care that isn’t required working the other way, yeah it’s legit, but that’s not what’s being complained about.

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Re:The Most Common Errors in Undergraduate Mathematics (2009) by watwut on Thursday November 19, 2020 @12:58PM (#25152228)
When you are doing equality and such all steps are reversible.

Working backwards is exactly the same as working forward. You develop reasoning where you see it easier until to figure out to connect sides.

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Re:The Most Common Errors in Undergraduate Mathematics (2009) by Caylio on Friday November 20, 2020 @01:12AM (#25157747)
Having equality signs at each step does not mean you can reverse the steps. You need bidirectional implication for that.
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