0.99r = 1
- Thread starter McDaniel
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0.9r <1
What makes sense is that 0.9r is so close to 1 that the difference is not measurable in a decimal value (it is however identifiable)
It's just a case of rounding up, a make do, it's close enough.
Hence why 0.3r is often referred to 1/3
Or why 0.9r is often referred to = 1
The fact is decimal calculations and fractions don't always mix/convert perfectly so you just have to make do and use whatever is the closest possible real variable that exists.
The difference is so negligible (infinitely small) between 0.9r and 1 that any resulting calculation ends up the same, as we do finite calculations.
If doing any mathematical calculation I'd happily take 0.9r to represent 1, although I know it doesn't, it just makes no sense to kick up a fuss about it, as using it as 1 works. This is why mathematicians happily accept 0.9r as being 1, It fits into the methods and calculations they use.
To actually believe 0.99r = 1 is just as acceptable as the world famous mathematician* Buzz Lightyear stating
It still doesn't alter the fact that 1>0.9r therefore 0.9r does not = 1
*May be fictional Toy Story character
What makes sense is that 0.9r is so close to 1 that the difference is not measurable in a decimal value (it is however identifiable)
It's just a case of rounding up, a make do, it's close enough.
Hence why 0.3r is often referred to 1/3
Or why 0.9r is often referred to = 1
The fact is decimal calculations and fractions don't always mix/convert perfectly so you just have to make do and use whatever is the closest possible real variable that exists.
The difference is so negligible (infinitely small) between 0.9r and 1 that any resulting calculation ends up the same, as we do finite calculations.
If doing any mathematical calculation I'd happily take 0.9r to represent 1, although I know it doesn't, it just makes no sense to kick up a fuss about it, as using it as 1 works. This is why mathematicians happily accept 0.9r as being 1, It fits into the methods and calculations they use.
To actually believe 0.99r = 1 is just as acceptable as the world famous mathematician* Buzz Lightyear stating
It still doesn't alter the fact that 1>0.9r therefore 0.9r does not = 1
*May be fictional Toy Story character
Wait let me get this right, its written on a pigeon in a plane that's on a treadmill inside another plane that's already taken off. At any point was there a helicopter on a turntable involved ?
Who said anything about doing a calculation. There is no calculation involved.
It is an equality formula, which holds true in aways.
Soldato
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yes! and the turntable was rotating contrary to the rotation of the helicopters rotor! Since both the turntable and the chopper got airborne....what was flying?
If they are not the same, define the difference.
Wrong? Both are finite and equivalent.
It has nothing to do with rounding. It has nothing to do with making things easier, or fitting into a method. It is just a fact.
Please don't argue otherwise, you are just wrong.
Soldato
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Can it not be quantified as a fraction, even if that particular fraction can't be written as a decimal? I assume there's a reason why it isn't? If the 9's never end as you say then we never truly reach 1? Don't get me wrong, I understand what's going on with 1 = 0.99r but the phrase "we never truly reach 1 no matter how many 9s we add on" is true is it not as we haven't actually reached it - otherwise why bother adding another 9 as all you'll do will get every so slightly closer/more accurate? Or is this something like a special law concerning infinity and that the formula 1 = 0.99r is a special case?
Also don't think I had an answer to my question 1 either
Cheers
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You are wrong at the very first statement. There is nothing stopping you having 1 number with 2 different symbols.
X= 2
Y= 2
There we have it, 2 symbols representing 1 number. Hardly difficult.
There is not a special case. You just have to understand infinity.
Another example.
What is the square root of 2? You actually have sereveral ways to represent this same entity.
Then what is the square root of 2 squared? 2 obviously.
Just like (1/3) * 3 = 1
A good way to look at this is to first properly understand the concept of infinity, try not to think of infinity as 'the end' but rather think of it as the lack of an end. With a lack of an end of a series of 9s there is a difference between it and 1 that is getting ever closer to 0.
Another way of thinking of it is of a ever growing string of 9s (after the 0.) think of it that every instance of time another 9 is being added to it and the 0.000... part is always trying to keep up with it but never will and so will be an evergrowing string of 0s and so is alwaus equal to 0 and if the diffetence beyween two numbers is 0 they are equal and so 0.99r = 1.
(A-Level Maths)
Also for people saying things can't be written in two ways
(n)^2 = (-n)^2
Another way of thinking of it is of a ever growing string of 9s (after the 0.) think of it that every instance of time another 9 is being added to it and the 0.000... part is always trying to keep up with it but never will and so will be an evergrowing string of 0s and so is alwaus equal to 0 and if the diffetence beyween two numbers is 0 they are equal and so 0.99r = 1.
(A-Level Maths)
Also for people saying things can't be written in two ways
(n)^2 = (-n)^2
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**** I understand it now!
so "0.99r" isn't a number, it's simply an algebraic representation which expresses the value of 1, a "symbol".
So "0.99r=1" is like saying "Pancake=1" or "Y=1" etc. ?
Why didn't anyone just say that in the first place?
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No its a decimal representation that represents the same Real number 1 (and I did say that earlier.)
Some numbers won't have a unique representation within a given number system.
For example - in say base 4:
0.333r = 1
That is not exactly what's was getting at but it is much closer to the mark.
There are 2 reasons why people get confused over 1= 0.9r
The first is that for some reason they think that the same number cannot have 2 different representations, which is clearly false.
Secondly they don't understand infinity, and instead think that infinity just means "a great very many huge number of things" it is not. You don't need something to exist in the universe to have a mathematical representation of it.
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Caporegime
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I think you're over-estimating your audience if you think that anyone is following this as it stands, let alone complicating matters further.
Caporegime
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This man for instance can barely type his own name and he's in his 50's.
These threads always go the same way.
People who studied maths up to GCSE = "It's not quite 1, it doesn't matter what maths trickery you use in the 'real world' it's not exactly the same, there'll always be a tiny bit left over"
People who know more maths = "They are the same".
People who studied maths up to GCSE = "It's not quite 1, it doesn't matter what maths trickery you use in the 'real world' it's not exactly the same, there'll always be a tiny bit left over"
People who know more maths = "They are the same".
I'm in 3rd year of maths degree, not really done many modules on this kind of thing but afaic it's just a flaw in recurring decimal notation.
I mean, to look at 0.99... it doesn't equal 1 but once you realise the limitation of writing down a recurring number you realise it does equal 1.
I don't understand why people that don't think 0.99...=1 yet are happy to think 0.33...= (1/3) (because by their same stupid logic 0.33... goes on forever so is never quite 1/3. Just utter pish).
Also i don't like the 'r' notation. 3 dots does the job.
I mean, to look at 0.99... it doesn't equal 1 but once you realise the limitation of writing down a recurring number you realise it does equal 1.
I don't understand why people that don't think 0.99...=1 yet are happy to think 0.33...= (1/3) (because by their same stupid logic 0.33... goes on forever so is never quite 1/3. Just utter pish).
Also i don't like the 'r' notation. 3 dots does the job.