Well, you seem to have forgotten that the woman in that video isn’t a Maths teacher, which would explain why she’s forgotten the rules of The Distributive Law and Terms.
until you gave up
I didn’t give up, you did.
I suggest we don’t do it again but instead, you review the thread
I suggest you check some Maths textbooks, instead of listening to a Physics major.
I don’t really care how many representations a number has, so long as those representations make sense. 2 = 02 = 2.0 = 1+1 = -1+3 = 8/4 = 2x/x. That’s all fine, we can use the basic rules of decimal notation to understand the first three, basic arithmetic to understand the next three, and basic algebra for the last one.
0.999… = 1 requires more advanced algebra in a pointed argument, or limits and infinite series to resolve, as well as disagreeing with the result of basic decimal notation. It’s steeped in misdirection and illusion like a magic trick or a phishing email.
I’m not blaming mathematicians for this, I am blaming teachers (and popular culture) for teaching that tools are inflexible, instead of the limits of those systems.
In this whole thread, I have never disagreed with the math, only it’s systematic perception, yet I have several people auguing about the math with me. It’s as if all math must be regarded as infinitely perfect, and any unbelievers must be cast out to the pyre of harsh correction. It’s the dogmatic rejection I take issue with.
Again, I don’t disagree with the math. This has never been about the math. I get that ever model is wrong, but some are useful. Math isn’t taught like that though, and that’s why people get hung up things like this.
Basic decimal notation doesn’t work well with some things, and insinuates incorrect answers. People use the tools they were taught to use. People get told they’re doing it wrong. People give up on math, stop trying to learn, and just go with what they can understand.
If instead we focus on the limitations of some tools and stop hammering people’s faces in with bigger equations and dogma, the world might have more capable people willing to learn.
Neither of those examples use the rules of those system though.
Basic arithmetic on decimap notation is performed by adding/subtracting each digit in each place, or multiplying each digit by each digit then adding those sub totals together, or the yet more complicated long division.
Adding (and by extension multiplying) requires the carry operation, because digits only go up to 9. A string of 9s requires starting at the smallest digit. 0.999… has no smallest digit, thus the carry operation fails to roll it over to 1. It’s a bug that requires more comprehensive methods to understand.
Someone using only basic arithmetic on decimal notation will conclude that 0.999… is not 1. Another person using only geocentrism will conclude that some planets follow spiral orbits. Both conclusions are wrong, but the fault lies with the tools, not the people using them.
simply accept that it has to be the case because 0.333… * 3. […] That is a correct mathematical understanding
This is my point, using a simple system (basic arithmetic) properly will give bad answers in specifically this situation. A correct mathematical understanding of arithmetic will lead you to say that something funky is going on with 0.999… , and without a more comprehensive understanding of mathematical systems, the only valid conclusions are that 0.999… doesn’t equal 1, or that basic arithmetic is limited.
So then why does everyone loose their heads when this happens? Thousands of people forcing algebra and limits on anyone they so much as suspect could have a reasonable but flawed conclusion, yet this thread is the first time I’ve seen anyone even try to mention the limitations of arithmetic, and they get stomped on.
Why is basic arithmetic so sacred that it must not be besmirched? Why is it so hard for people to admit that some tools have limits? Why is everyone bringing in so many more advanced systems when my entire argument this whole time is that a simple system has limits?
That’s my whole argument. Firstly, that 0.999… catches people because using arithmetic properly leads to an incorrect understanding of repeating decimals. And secondly, that starting with the limits of arithmetic will increase understand with less frustration than throwing more complicated solutions around.
My argument have never been with the math, only with our perceptions of it and how we go about teaching it.
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Very rarely wrong actually.
The only people who think there’s something wrong with PEMDAS are people who have forgotten one or more rules of Maths.
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Well, you seem to have forgotten that the woman in that video isn’t a Maths teacher, which would explain why she’s forgotten the rules of The Distributive Law and Terms.
I didn’t give up, you did.
I suggest you check some Maths textbooks, instead of listening to a Physics major.
P.S. you proved my point
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BWAHAHAHA! I see you still didn’t learn to check facts first. 😂😂😂
P.S.
Yep, Maths teachers do it right. :-)
I don’t really care how many representations a number has, so long as those representations make sense. 2 = 02 = 2.0 = 1+1 = -1+3 = 8/4 = 2x/x. That’s all fine, we can use the basic rules of decimal notation to understand the first three, basic arithmetic to understand the next three, and basic algebra for the last one.
0.999… = 1 requires more advanced algebra in a pointed argument, or limits and infinite series to resolve, as well as disagreeing with the result of basic decimal notation. It’s steeped in misdirection and illusion like a magic trick or a phishing email.
I’m not blaming mathematicians for this, I am blaming teachers (and popular culture) for teaching that tools are inflexible, instead of the limits of those systems.
In this whole thread, I have never disagreed with the math, only it’s systematic perception, yet I have several people auguing about the math with me. It’s as if all math must be regarded as infinitely perfect, and any unbelievers must be cast out to the pyre of harsh correction. It’s the dogmatic rejection I take issue with.
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Again, I don’t disagree with the math. This has never been about the math. I get that ever model is wrong, but some are useful. Math isn’t taught like that though, and that’s why people get hung up things like this.
Basic decimal notation doesn’t work well with some things, and insinuates incorrect answers. People use the tools they were taught to use. People get told they’re doing it wrong. People give up on math, stop trying to learn, and just go with what they can understand.
If instead we focus on the limitations of some tools and stop hammering people’s faces in with bigger equations and dogma, the world might have more capable people willing to learn.
Removed by mod
Neither of those examples use the rules of those system though.
Basic arithmetic on decimap notation is performed by adding/subtracting each digit in each place, or multiplying each digit by each digit then adding those sub totals together, or the yet more complicated long division.
Adding (and by extension multiplying) requires the carry operation, because digits only go up to 9. A string of 9s requires starting at the smallest digit. 0.999… has no smallest digit, thus the carry operation fails to roll it over to 1. It’s a bug that requires more comprehensive methods to understand.
Someone using only basic arithmetic on decimal notation will conclude that 0.999… is not 1. Another person using only geocentrism will conclude that some planets follow spiral orbits. Both conclusions are wrong, but the fault lies with the tools, not the people using them.
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This is my point, using a simple system (basic arithmetic) properly will give bad answers in specifically this situation. A correct mathematical understanding of arithmetic will lead you to say that something funky is going on with 0.999… , and without a more comprehensive understanding of mathematical systems, the only valid conclusions are that 0.999… doesn’t equal 1, or that basic arithmetic is limited.
So then why does everyone loose their heads when this happens? Thousands of people forcing algebra and limits on anyone they so much as suspect could have a reasonable but flawed conclusion, yet this thread is the first time I’ve seen anyone even try to mention the limitations of arithmetic, and they get stomped on.
Why is basic arithmetic so sacred that it must not be besmirched? Why is it so hard for people to admit that some tools have limits? Why is everyone bringing in so many more advanced systems when my entire argument this whole time is that a simple system has limits?
That’s my whole argument. Firstly, that 0.999… catches people because using arithmetic properly leads to an incorrect understanding of repeating decimals. And secondly, that starting with the limits of arithmetic will increase understand with less frustration than throwing more complicated solutions around.
My argument have never been with the math, only with our perceptions of it and how we go about teaching it.
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