Motor Daddy
Valued Senior Member
It is interesting how a simple quirk created by expressing one third in base ten can baffle so many people.
Probably blows their mind to see that 2/7 = .285714r and 5/7 = .714285r. Therefore 2/7 + 5/7 = .999999r
It is interesting how a simple quirk created by expressing one third in base ten can baffle so many people.
Probably blows their mind to see that 2/7 = .285714r and 5/7 = .714285r. Therefore 2/7 + 5/7 = .999999r
See thar little "r" at the end? That means repeating.What is really interesting is that you swept a remainder of .000002 under the rug and claimed 2 divided by 7 was .285714r.
Let me clarify your mistake. That .285714 is with a remainder of .000002.
You did not complete the division of 2 divided by 7 because you never divided the remainder equally at ANY point in the division.
If the remainder would have been divided equally then the division would not continue.
So it appears YOU are the one BAFFLED by simple long division you learn in 2nd grade!
Obviously a retorical questionSeriously, are you that stupid or are you just a troll?
See thar little "r" at the end? That means repeating.
Seriously, are you that stupid or are you just a troll?
He's pretending he doesn't know that in maths the sum of an infinite series can converge to a finite value. It's rather like not understanding what an asymptote is, in a graph.See thar little "r" at the end? That means repeating.
Seriously, are you that stupid or are you just a troll?
I addressed this in post #140.Moron,
Every decimal place to the right is 10 times smaller.
0.01 is 10 times smaller than 0.1
0.1 is 1 Tenth
0.01 is 1 Hundredth
0.001 is 1 Thousandth
0.9 is 9 Tenths
0.09 is 9 Hundredths
0.009 is 9 Thousandths
.99 is 99 Hundredths = 99/100
.999 is 999 Thousandths = 999/1,000
.9999 is 9,999 Ten Thousandths = 9,999/10,000
.99999 is 99,999 Hundred Thousandths = 99,999/100,000
.999999 is 999,999 Millionths = 999,999/1,000,000
They are ALL less than 1.0
The more 9's you place after the decimal point, the closer you are to 1.0, but you can never be equal to 1.0 by placing more 9's after a decimal point.
.999999999999999999 = 999,999,999,999,999,999/1,000,000,000,000,000,000
That does NOT equal 1.0
How could you be so F'n stupid?
This is only true for a finite n.View attachment 4942
Here is the example for .9R.
Common practice truncates any sequence when it satisfies the precision requirements.
I don't understand your difficulty. Surely you are familiar with the idea of an asymptote, are you not?forum;
The 'square circle' title got my attention since I exchange posts with someone on another forum who proposes a square light clock.
The repeating decimal problem has appeared on most of the forums visited, with the same response, and is on my list of annoying topics.
I read all pages 1-9.
Motor Daddy was correct some of the time and wrong some of the time.
Dividing by n depends on what is divided.
Examples:
If the task is to divide a collection of 10 objects into 3 equal parts, it's not possible.
You will get 3+3+3+1. You divide the collection, but not the parts. If the material is continuous like a fluid, you can divide it into n equal portions.
A circle (pie) can be divided into n equal parts if n is a factor of 360.
Division of geometrical shapes depends on symmetries.
Equal is understood to mean without defined significant differences.
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No one asks, why did the earlier mathematicians define 'limits' instead of declaring an equality? Primarily because of their experience with sequences.
a=sequence of terms a(n), either a term after n recursive applications of a function or a summation of n terms. In words, the limit of (a), as n (increases without limit), is L.
The phrase in parentheses is substituted for 'approaches infinity', a totally nonsensical term. You can't approach something that is unreachable (the horizon, a carrot on a stick, etc).
If infinity means without bounds, then there is no end. If there is no last term, then the sequence remains incomplete, and the current value is always an approximation. Many know and state 'infinity is not a number' then contradict themselves by using it in that sense.
If a result requires an 'infinite' number of clock cycles, it never happens.
In agreement with Motor Daddy, no one will ever see an exact value of pi, or an irrational number. They only exist as abstract entities in the world of pure math.
View attachment 4941
Here is a definition of 'limit' which I posted to mathforums, which they rejected (even after telling them it is from a lesson plan from the math dept. at MIT. It shows the degree of arrogance in their 'fraternity', and places them above physicsforums.
View attachment 4942
Here is the example for .9R.
Common practice truncates any sequence when it satisfies the precision requirements.
A circle (pie) can be divided into n equal parts if n is a factor of 360.
Aren't 100% and 360 degrees just man-made conventions that have been chosen for our convenience? Couldn't we arbitrarily say that one pizza is equal to 99 Neddy units, and therefore 1/3 of the pizza is 33 Neddy units?
If you are only considering a finite number of elements in such an infinite sequence, you will get close to, but not equal to, its limit...
If you disagree that 0.999... = 1 then surely you must think that there is a number between 0.999... and 1? Care to say what it is? For all A and B, where A and B are different numbers, there exists another number (A+B)/2 which lies between A and B. So what is it for 0.999... and 1?
Surely you are familiar with the idea of an asymptote, are you not?
But Motor Daddy told me that I can't cut one pizza into three equal parts, because one pizza is 100%, and 100 is not evenly divisible by 3, according to him.
Percent means 'parts per 100' (latin 'centum', roman numeral c), i.e. a ratio.
This is something that can be done with a compass. The circumference is magenta. At points 1, 2, 3, draw a gray circle of radius r. This divides the circle into 3 equal sectors of 120 deg. Maybe MD didn't study geometry.
View attachment 4945
You can consider it, and it does exist. The sum of the sequence really is 1. Not "almost 1" but actually 1.You gave the answer in the first line above. You can't consider the complete sequence, because it doesn't exist. Another instance of 'all things thinkable are not realizable'.
So what?Performing the division above you get more sequences of 9's.
Yes, it is an infinite sequence, so stop being dishonest and only considering the first n finite elements of the sequence, rather than all of them.The context is 'infinite sequence', without an end/boundary. There is no last '9'. There is no such thing as a 'thing without boundaries'. It's a contradiction of terms. Boundaries are what enables measurements including counting. You lose your perspective when expecting a number different from '9'.
No, it wouldn't.If the sequence were an odometer, the only way it would roll over to 1 would be the addition of 1 at some position, but that is prohibited by its definition.
It becomes zero. That is what it means for it to reach its limit at infinity.The small difference is never zero, so the last line states 'for all n'.
So what? We still have this concept of infinity. All you are doing is refusing to look at that and instead stick with a finitie number of elements as if that disproves the case for the infinite.Most math people agree, there is no greatest integer n.
There really is no problem, other than your misunderstanding of maths.The root cause of this problem is the concept of 'continuum'.