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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 theyβre 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 0.999β¦ 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 theyβre 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?
This isnβt about limits of accuracy
According to who? Where does it say what it's about? It doesn't.
please show me how basic arithmetic can make 0.999
You still haven't shown why you're limiting yourself to basic arithmetic. There isn't anything at all in the meme to indicate it's about basic arithmetic only. It's just some Maths statements with no context given.
then a correct use of the system must be applicable to everything, right?
Different systems for different applications. Sometimes multiple systems for one problem (e.g. proofs).
You shouldnβt need a new system like algebra to be correct, right?
Limits of accuracy isn't algebra.
This isnβt about limits of accuracy
According to who?
According to me, talking about the origin of the 0.999... issue of the original comment, the "conversion of fractions to decimals", or using basic arithmetic to manipulate values into repeating decimals. This has been my position the entire time. If this was about the limits of accuracy, then it would be impossible to solve the 0.999... = 1 issue. Yet it is possible, our accuracy isn't limited in this fashion.
You still haven't shown why you're limiting yourself to basic arithmetic.
Because that's where the entire 0.999... = 1 originates. You'll never even see 0.999... without using basic addition on each digit individually, especially if you use fractions the entire time. Thus 0.999... is an artifact of basic arithmetic, a flaw of that system.
Different systems for different applications.
Then you agree that not every system is applicable everywhere! Even if you use that system perfectly, you'll still end up with the wrong answer! Thus the issue isn't someone using the system incorrectly, it's a limitation of the system that they used. The correct response to this isn't throwing heaps of other systems at the person, it's communicating the limit of that system.
If someone is trying to hammer a screw, chastising them for their swinging technique then using your personal impact wrench in front of them isn't going to help. They're just going to hit you with the hammer, and continue using the tools they have. Explaining that a hammer can't do the twisting motion needed for screws, then handing them a screwdriver will get you both much farther.
Limits of accuracy isn't algebra.
It never was, and neither is the problem we've been discussing. You can talk about glue, staples, clamps, rivets, and bolts as much as you like, people with hammers are still going to hit screws.
According to me, talking about the origin of the 0.999β¦
Right. So not according to the meme, which doesn't tell us where the 0.999... comes from. Nor the 1 - could be an integer, floating point, or an estimation. Thanks for playing.