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silly Old Math has .999... = 1, while New Math has .999... is always a tiny bit smaller than 1//proof included
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Archimedes Plutonium
May 26, 2017, 6:21:45 PM5/26/17
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In New Math, we define Infinity precisely with a borderline, so the stupid argument that .9999... is somehow equal to 1 never passes the test. When you have a border between finite and infinite, you cannot screw the mind in thinking .9999.... somehow, magically turns into 1.
NEW MATH uncovers the .9999..... screwy logic
The borderline in New Math where finite end and infinity begins is 1*10^604
So in 10 Grid where we pretend 10 is the borderline the number 9.9 is the last number before you reach 10. In Old Math, their poor logic would say 9.9 = 10. When you well define infinity, you cannot be screwy any more, for 9.9 + .1 = 10. And in 10 Grid .9 +.1 = 1
Doing the same for 100 Grid we have 99.99 +.01 = 100 and where .99 + .01 = 1
Doing the same for 1000 Grid we have 999.999 + .001 = 1000, and where .999 + .001 = 1
Never is the case, never is the situation where .9999.... =1. Never. And the reason is obvious, that when you Well Define what it means to be infinite by establishing the infinity borderline, you cannot hide from arithmetic in that .999.... is always short of 1.
When you act dumb, play dumb, play lazy and do not Well Define what infinity is, you come up with this screwy, lazy, stupid game of .999... is 1.
Proof in New Math with its well defined Infinity borderline.
.9 times 5 is 4.5
.99 times 5 is 4.95
.999 times 5 is 4.995
.9999 times 5 is 4.9995
.99999 times 5 is 4.99995
.
.
.
In Old Math, their stupid silly argument when you multiply 5 times .9999.... that you somehow magically get rid of that pestering 5 digit on the end of the string there. That you somehow removed the 5 digit because you play the silly game that you are in "infinity territory and waving a magic wand, gets rid of the 5 digit" And many, or most people have loose marbles in their logic head to accept that crazy argument. Old Math always comes in and uses Infinity to whatever bully way they want to use it, because they were too lazy to well define infinity with a borderline and outright too stupid, far too stupid to actually determine the borderline and recognize that Grid Systems prevent the argument of "well, let's just scrub away the 5 ending digit".
Same crazy argument in .9999.... = 1 as in the Oresme harmonic series argument. Two crazies put together, and welcome to Old Math. If you are dumb and silly to buy .999...= 1 , well, you no doubt are that dumb and silly to buy the idea that 1 + 1/2 + 1/3 + 1/4 + 1/5 + . . . diverges and does not converge. If you have any logical commonsense in your mind, you would realize that the smallest series to diverge is the series 1+1+1+1+.... for that is the Natural Numbers and they are the smallest infinite set to diverge. If you have a series that consists of fractions of 1, you just are never going to reach the infinity borderline.
So the Harmonic Series in New Math is this::
1 + 1/2 + 1/3 + . . + 1/10 and does that equal or surpass 10? Obviously not
1 + 1/2 + 1/3 + . . + 1/100 and does that equal or surpass 100? Obviously not
1+1/2 +1/3 + . . + 1/1000 and does that equal or surpass 1000? Obviously not
This is what happens in mathematics when logical goonclods dictate what math is, when it is nothing like that.
When you never define infinity precisely with a borderline, then the goonclod squad comes in and dictates to rational people, commonsense people, dictates to them that Harmonic Series surpasses infinity by diverging and that .9999... equals 1 when that commonsense person knows that is screwy.
Old Math is screwy, screw screw Mathematics.
AP
NEW MATH uncovers the .9999..... screwy logic
The borderline in New Math where finite end and infinity begins is 1*10^604
So in 10 Grid where we pretend 10 is the borderline the number 9.9 is the last number before you reach 10. In Old Math, their poor logic would say 9.9 = 10. When you well define infinity, you cannot be screwy any more, for 9.9 + .1 = 10. And in 10 Grid .9 +.1 = 1
Doing the same for 100 Grid we have 99.99 +.01 = 100 and where .99 + .01 = 1
Doing the same for 1000 Grid we have 999.999 + .001 = 1000, and where .999 + .001 = 1
Never is the case, never is the situation where .9999.... =1. Never. And the reason is obvious, that when you Well Define what it means to be infinite by establishing the infinity borderline, you cannot hide from arithmetic in that .999.... is always short of 1.
When you act dumb, play dumb, play lazy and do not Well Define what infinity is, you come up with this screwy, lazy, stupid game of .999... is 1.
Proof in New Math with its well defined Infinity borderline.
.9 times 5 is 4.5
.99 times 5 is 4.95
.999 times 5 is 4.995
.9999 times 5 is 4.9995
.99999 times 5 is 4.99995
.
.
.
In Old Math, their stupid silly argument when you multiply 5 times .9999.... that you somehow magically get rid of that pestering 5 digit on the end of the string there. That you somehow removed the 5 digit because you play the silly game that you are in "infinity territory and waving a magic wand, gets rid of the 5 digit" And many, or most people have loose marbles in their logic head to accept that crazy argument. Old Math always comes in and uses Infinity to whatever bully way they want to use it, because they were too lazy to well define infinity with a borderline and outright too stupid, far too stupid to actually determine the borderline and recognize that Grid Systems prevent the argument of "well, let's just scrub away the 5 ending digit".
Same crazy argument in .9999.... = 1 as in the Oresme harmonic series argument. Two crazies put together, and welcome to Old Math. If you are dumb and silly to buy .999...= 1 , well, you no doubt are that dumb and silly to buy the idea that 1 + 1/2 + 1/3 + 1/4 + 1/5 + . . . diverges and does not converge. If you have any logical commonsense in your mind, you would realize that the smallest series to diverge is the series 1+1+1+1+.... for that is the Natural Numbers and they are the smallest infinite set to diverge. If you have a series that consists of fractions of 1, you just are never going to reach the infinity borderline.
So the Harmonic Series in New Math is this::
1 + 1/2 + 1/3 + . . + 1/10 and does that equal or surpass 10? Obviously not
1 + 1/2 + 1/3 + . . + 1/100 and does that equal or surpass 100? Obviously not
1+1/2 +1/3 + . . + 1/1000 and does that equal or surpass 1000? Obviously not
This is what happens in mathematics when logical goonclods dictate what math is, when it is nothing like that.
When you never define infinity precisely with a borderline, then the goonclod squad comes in and dictates to rational people, commonsense people, dictates to them that Harmonic Series surpasses infinity by diverging and that .9999... equals 1 when that commonsense person knows that is screwy.
Old Math is screwy, screw screw Mathematics.
AP
Archimedes Plutonium
May 26, 2017, 9:28:36 PM5/26/17
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Rational people need to counter the stupid hornswaggle argument proposed by fools, establishment cornballs
Archimedes Plutonium
May 27, 2017, 1:26:22 AM5/27/17
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Now in the history of sci.math since 1993 when I started as a subscriber, the topic most often seen is perhaps the .999... = 1 debate. Since it is so common, I endeavor to keep it in the public eye as to why it is so pulverizingly dumb. Why .999... is never equal to 1 but just close or near 1.
We have seen the argument given by cads of Old Math, where they manipulate algebra. But algebra manipulation is not a proof, but is rather a distortion. When you start out assuming .999... =1, you can easily distort and corrupt the argument. Say, multiply by 10 gives 9.999... = 10, and thus say .9999... has to be 1 so that 9+1 = 10. That is a pitiful circular argument.
We could easily say on the other side of the argument that multiply by 5 instead of 10. We have thence
4.9999...995 = 5. We do not have a 4.9999....999, for we have that nagging 5 digit we cannot get rid of.
All of which is solved if we realize infinity needs to have a borderline to well define infinity. Once you have a border, then never is the case that .9999...99 is equal to 1, for it is always a tad shy of 1.
So this message should appear frequently in sci.math to counter the crazy fools who think .999.. is actually the same as 1. The very same fools that thought the Harmonic Series 1 + 1/2 + 1/3, . . . diverges and surpasses infinity.
These irrational punks of logic would be the same misfits of thought who say that a fraction of a full pie exceeds the full pie itself. So handed a 1/12 of a cherry pie, these thinkers would think that 1/12 is larger than 1 itself.
AP
We have seen the argument given by cads of Old Math, where they manipulate algebra. But algebra manipulation is not a proof, but is rather a distortion. When you start out assuming .999... =1, you can easily distort and corrupt the argument. Say, multiply by 10 gives 9.999... = 10, and thus say .9999... has to be 1 so that 9+1 = 10. That is a pitiful circular argument.
We could easily say on the other side of the argument that multiply by 5 instead of 10. We have thence
4.9999...995 = 5. We do not have a 4.9999....999, for we have that nagging 5 digit we cannot get rid of.
All of which is solved if we realize infinity needs to have a borderline to well define infinity. Once you have a border, then never is the case that .9999...99 is equal to 1, for it is always a tad shy of 1.
So this message should appear frequently in sci.math to counter the crazy fools who think .999.. is actually the same as 1. The very same fools that thought the Harmonic Series 1 + 1/2 + 1/3, . . . diverges and surpasses infinity.
These irrational punks of logic would be the same misfits of thought who say that a fraction of a full pie exceeds the full pie itself. So handed a 1/12 of a cherry pie, these thinkers would think that 1/12 is larger than 1 itself.
AP
Don Redmond
May 27, 2017, 12:09:24 PM5/27/17
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Don
Markus Klyver
May 27, 2017, 12:17:20 PM5/27/17
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Archimedes Plutonium
May 27, 2017, 6:05:59 PM5/27/17
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On Saturday, May 27, 2017 at 11:09:24 AM UTC-5, Don Redmond wrote:
(snipped)
Old Math has the leak of .999.... =1 for multiply by 5 and you have the nasty 4.999...995 digit of 5 on trailing end, like a rust spot leaking in the bucket
Old Math has the Harmonic Series of 1 + 1/2 + 1/3 +1/4 +.... where given any N, the pitiful series is just a tiny tiny microscopic size of N for large N. But then, you have half crazy mathematicians willing to stake their careers to the idea that such a series diverges. We think of moths flying into a light beam to singe their wings and death, we think of those moths as "they cannot help themselves"
Likewise, our math education system of math professors so dumb and stupid in logic that they want to acknowledge the Series is microscopic compared to large N, yet, on the other hand, they like moths want to believe the series totals up to infinity itself. At least the moth has more brains than the Old Math math professor, for the moth is compelled by instinct. The math professor is compelled only by his stupidity.
AP
(snipped)
>
> Why does 1 + 1/2 + ... + 1/n not greater than n imply convergence? If n > e^10, then this sum is > 10. Shouldn't thius count for something?
>
> Don
Old Math reminds me of the old bucket that has leaks and rust, and you have to use it, only because there are no other buckets around.
> Why does 1 + 1/2 + ... + 1/n not greater than n imply convergence? If n > e^10, then this sum is > 10. Shouldn't thius count for something?
>
> Don
Old Math has the leak of .999.... =1 for multiply by 5 and you have the nasty 4.999...995 digit of 5 on trailing end, like a rust spot leaking in the bucket
Old Math has the Harmonic Series of 1 + 1/2 + 1/3 +1/4 +.... where given any N, the pitiful series is just a tiny tiny microscopic size of N for large N. But then, you have half crazy mathematicians willing to stake their careers to the idea that such a series diverges. We think of moths flying into a light beam to singe their wings and death, we think of those moths as "they cannot help themselves"
Likewise, our math education system of math professors so dumb and stupid in logic that they want to acknowledge the Series is microscopic compared to large N, yet, on the other hand, they like moths want to believe the series totals up to infinity itself. At least the moth has more brains than the Old Math math professor, for the moth is compelled by instinct. The math professor is compelled only by his stupidity.
AP
Markus Klyver
May 27, 2017, 6:17:43 PM5/27/17
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Are you actually suggesting the harmonic series converges? Towards what, then?
Archimedes Plutonium
May 27, 2017, 6:49:08 PM5/27/17
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On Saturday, May 27, 2017 at 5:17:43 PM UTC-5, Markus Klyver wrote:
> Are you actually suggesting the harmonic series converges? Towards what, then?
Well, you first have to well define infinity, something you never did in all your life.
> Are you actually suggesting the harmonic series converges? Towards what, then?
You just opined what infinity means to you, and opined that other people who opined infinity.
You had but a mere notion of what infinity means. You never made infinity be a mathematical precision definition.
When it came to something like .9999...9999....999 you opined it was 1 and you had plenty of consort opinionated others to opine with you.
There is one and only one way to PRECISELY define infinity, that is, a borderline between finite and infinite.
You can find this number in mathematics itself. Math leads a path to a border between finite and what is infinite. The Tractrix leads us to a number 1*10^604, and it coincides with the fact that at this number pi digits have 3 zeroes in a row. The area inside a circle equals the area in a respective tractrix when this number 1*10^-604 is reached. For the first time in a Tractrix Life, if a figure can have a life, does the area of the tractrix catch-up and equal the area of the circle. Since, tractrix area equaling circle area means infinity, well, you reached infinity.
All series in math and all sequences in math employ Infinity concept. So if you, Markus has a opinion of infinity and never a well defined infinity, then of course, you make the stupid decision that .999... is equal to 1 and make the horrendously stupid decision that Harmonic Series diverges.
But if you realize infinity has a borderline, then at infinity border of 1*10^604, the harmonic series is no more than about approx 2.3 x 604 = 1390.7
And where .999... multiply by 5 is 4.999...995 where the 5 digit is in the 10^-604 place value, and that definitely is not 5 itself but a tiny shaving off.
Your problem Markus, is that you want to go through life with a cloudy, crappy opinion of what infinity is. You use infinity to sweep under the rug all sorts of math phantasies, not math reality.
Math is the science of precision, and when you do not have infinity precisely defined by a borderline between it and finite, well, you are not doing math, but some fantasy delusion of math.
AP
Markus Klyver
May 27, 2017, 6:51:53 PM5/27/17
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Archimedes Plutonium
May 27, 2017, 7:13:01 PM5/27/17
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On Saturday, May 27, 2017 at 5:51:53 PM UTC-5, Markus Klyver wrote:
>
> Are you saying that there're no numbers smaller than 10^-604 and bigger than 10^604? What's 10^604 +1, according to you?
The only numbers mathematics can use are Rational numbers. There exists numbers beyond infinity border and numbers between the gaps of 1*10^-604, but these are all infinite and irrational numbers.
>
> Are you saying that there're no numbers smaller than 10^-604 and bigger than 10^604? What's 10^604 +1, according to you?
They take up space, for in True Math, there are gaps between numbers.
Just like Physics, we can only talk about momentum precisely but not position precisely. Physics is quantum with gaps and holes in between. Physics is larger than math and contains math. Since physics is riddled with holes, math is riddled with holes.
In New Math, true math, there is no continuum, that is just a fairy tale, a fire breathing dragon. There is no curve in math but rather tiny straightline segments connected like a chain link. The circle does not exist but rather a many sided regular polygon whose sides are so tiny that you visualize them as a smooth curve.
None of this should bother you, for our world is mostly no larger in reflection and understanding than what the 10^5 Grid is all about. Bacteria and Virus are no smaller than numbers in the 10^20 Grid, while infinity is 10^604 Grid.
The circle you see on a Computer screen is no more than the 10^5 Grid.
Trouble with your life in math so far, Markus, is that you have not been taught to think logically and think clearly. You have been spoon fed crap in school and cannot break out of your shell of ideas= opinion.
Take a break,-- I have other matters to attend to.
AP
Markus Klyver
May 27, 2017, 7:38:37 PM5/27/17
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So all numbers larger than 10^604 are infinite and irrational?
Archimedes Plutonium
May 27, 2017, 11:56:37 PM5/27/17
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On Saturday, May 27, 2017 at 6:38:37 PM UTC-5, Markus Klyver wrote:
> So all numbers larger than 10^604 are infinite and irrational?
Did you know, probably not that 0 is infinite and irrational.
> So all numbers larger than 10^604 are infinite and irrational?
We define Rational as "ratio" being able to put into a ratio.
Since 1, 2 ,3 are put into a ratio, 1/1, 1/2, 2/1, 1/3, 3/2, 3/1, 2/3, 3/2, hope I left none out.
Now, put 0 into a ratio. Acceptable for 0/1 but not 1/0 nor 0/0.
So, we define Rational as ratio but 0 cannot be a rational number.
AP
peek...@gmail.com
May 28, 2017, 1:40:59 AM5/28/17
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Markus Klyver
May 28, 2017, 3:44:17 AM5/28/17
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So now all of the sudden 0 is irrational?
Archimedes Plutonium
May 28, 2017, 4:21:44 AM5/28/17
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The number 0 has always been irrational. You have not applied the meaning of What is Rational to 0. You looked at 0 and opined-- it is Rational.
You put 1 and 2 through the ratio test 1/1 , 2/1 , 1/2 and said they pass the test.
You never put 0 through the ratio test and realized 1/0 is not a ratio. So what were you doing in school all that time-- looking at the girls. Certainly not looking or thinking about numbers.
AP
You put 1 and 2 through the ratio test 1/1 , 2/1 , 1/2 and said they pass the test.
You never put 0 through the ratio test and realized 1/0 is not a ratio. So what were you doing in school all that time-- looking at the girls. Certainly not looking or thinking about numbers.
AP
Markus Klyver
May 28, 2017, 5:10:24 AM5/28/17
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Being rational means it can be written as a fraction of integers. 0 can be written as a fraction of integers, hence 0 is rational.
Archimedes Plutonium
May 28, 2017, 5:27:20 AM5/28/17
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Hello Don let me ask a question in the same vain as yours.
Knowing how sappy Old Math is on the Harmonic series thinking it diverges.
But is Old Math double sappy. Do they in Old Math consider a Series composed of all terms greater than 1 as converging at infinity. You see Don you can never underestimate the silly ideas of Old Math,
In New Math the smallest divergent series is 1+1+1+....
So i would not be surprized that in Old Math they thought 2 + 1.5 + 1.25 + 1.125+ . . . Converges.
Please tell me Old Math was sane on that score.
But then, Don, something I brought up years ago in that Old Math believes Harmonic series diverges is that Old Math cannot have a smallest Divergent series. And that is a big hole-in-head of Old Math. Now by smallest i mean a smallest Constant Series where every term is the same.
In 10 Grid the smallest divergent series is 1+ addig 1 ten times and the smallest convergent series is .9+ adding .9 ten times is 9. Remember smallest constant series.
Yet Old Math cannot support a Smallest divergent or convergent constant series. And that has to be a gigantic flaw in Old Math.
AP
Knowing how sappy Old Math is on the Harmonic series thinking it diverges.
But is Old Math double sappy. Do they in Old Math consider a Series composed of all terms greater than 1 as converging at infinity. You see Don you can never underestimate the silly ideas of Old Math,
In New Math the smallest divergent series is 1+1+1+....
So i would not be surprized that in Old Math they thought 2 + 1.5 + 1.25 + 1.125+ . . . Converges.
Please tell me Old Math was sane on that score.
But then, Don, something I brought up years ago in that Old Math believes Harmonic series diverges is that Old Math cannot have a smallest Divergent series. And that is a big hole-in-head of Old Math. Now by smallest i mean a smallest Constant Series where every term is the same.
In 10 Grid the smallest divergent series is 1+ addig 1 ten times and the smallest convergent series is .9+ adding .9 ten times is 9. Remember smallest constant series.
Yet Old Math cannot support a Smallest divergent or convergent constant series. And that has to be a gigantic flaw in Old Math.
AP
Markus Klyver
May 28, 2017, 5:40:00 AM5/28/17
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So what does it converge towards, then?
Archimedes Plutonium
May 28, 2017, 5:41:25 AM5/28/17
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Correction in the post i made to Don, i meant largest convergent series. But there can be a concept of the smallest convergent series if we eliminate 0.
Now the concept of Rational is ratio. So if 1/0 is undefined then that means 0 is not a ratio and not Rational. Not even a philosopher would make that mistake.
AP
Now the concept of Rational is ratio. So if 1/0 is undefined then that means 0 is not a ratio and not Rational. Not even a philosopher would make that mistake.
AP
Markus Klyver
May 28, 2017, 5:49:34 AM5/28/17
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But we can write 1 as a ratio of integers, namely 1/1.
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