those systems are giving an incorrect answer
When there’s an incorrect answer it’s because the user has made a mistake.
Instead of telling those people they’re wrong
They were wrong, and I told them where they went wrong (did something to one side of the equation and not the other).
The system I’m talking about is elementary decimal notation and basic arithmetic. Carry the 1 and all that. Equations and algebra are more advanced and not taught yet.
There is no method by which basic arithmetic and decimal notation can turn 0.999… into 1. All of the carry methods require starting at the smallest digit, and repeating decimals have no smallest digit.
If someone uses these systems as they were taught, they will get told they’re wrong for doing so. If we focus on that person being wrong, then they’re more likely to give up on math entirely, because they’re wrong for doing as they were taught. If we focus on the limitstions of that system, then they have the explanation for the error, and an understanding of why the more complicated system is preferable.
All models are wrong, but some are useful.
not taught yet
What do you mean not taught yet? There’s nothing in the meme to indicate this is a primary school problem. In fact it explicitly has a picture of an adult, so high school Maths is absolutely on the table.
There is no method by which basic arithmetic and decimal notation can turn 0.999… into 1.
In high school we teach that they are the same thing. i.e. limits of accuracy, 1 isn’t the same thing as 1.000…, but rather 1+/- some limit of accuracy (usually 1/2). Of course in programming it matters if you’re talking about an integer 1 or a floating point 1.
If someone uses these systems as they were taught, they will get told they’re wrong for doing so
The only people I’ve seen get things wrong is people not using the systems correctly (such as the alleged “proof” in this thread, which broke several rules of Maths and as such didn’t prove anything), and it’s a teacher’s job to point out how to use them correctly.
What do you mean not taught yet?
I mean those more advanced methods are taught after basic arithmetic. There are plenty of adults that operate primarily with 5th grade math, and a scary number of them do finances…
limits of accuracy
This isn’t about limits of accuracy, we’re working with abstract values and ideal systems. Any inaccuracies must be introduced by those systems.
If you think the system isn’t at fault here, please show me how basic arithmetic can make 0.999… into 1. Show me how the carry method deals with Infinity correctly. If every error is just using the system incorrectly, then a correct use of the system must be applicable to everything, right? You shouldn’t need a new system like algebra to be correct, right?
