# Naked Science Forum

## On the Lighter Side => New Theories => Topic started by: sim on 10/01/2019 11:35:30

Title: Mathematics proven inconsistent an integer= a non-integer
Post by: sim on 10/01/2019 11:35:30
1)Mathematics/science end in contradiction - an integer= a non-integer. When mathematics/science end in contradiction it is proven in logic that you can prove anything you want in mathematics ie you can prove Fermat's last theorem and you can disprove Fermats last theorem

The paper proves  1=0.999...-thus maths ends in contradiction
when
1 is a finite number it stops
A finite decimal is one that stops, like 0.157
A non-finite decimal like 0.888.. does not stop
A non-finite decimal like 0.999... does not stop
when a finite number 1 = a non-finite number 0.999.. then maths ends in contradiction

another way
1 is an integer a whole number
0.888... is a non-integer it is not a whole number
0.999... is a non-integer not a whole number
when a integer 1 =a non-integer 0.999... maths ends in contradiction
Title: Re: Mathematics proven inconsistent an integer= a non-integer
Post by: Bored chemist on 10/01/2019 12:33:13
and you can disprove Fermats last theorem
Go on then...
Incidentally, the 0.999... =1 thing just shows that there are two ways of writing the same number.
Not a problem with maths, a minor problem with our  writing system.
Title: Re: Mathematics proven inconsistent an integer= a non-integer
Post by: guest4091 on 10/01/2019 18:24:38
when a integer 1 =a non-integer 0.999... maths ends in contradiction
Was that you on Sciforums?
The problem is knowing the difference between an equality and a limit. They are not equivalent!
Title: Re: Mathematics proven inconsistent an integer= a non-integer
Post by: evan_au on 10/01/2019 21:14:31
I can explain why 1 = 0.9999.

0.9999. = 9/10 + 9/100 + 9/1000 + ....
- This is a "Geometric series" = a + a*r + a*r2 + a*r3 + ...
- In this case, with initial value a=9/10 and ratio between successive terms =1/10.
- The sum of an arbitrary geometric series = a/(1-r) = (9/10)/(1-1/10) = (9/10)/(9/10) = 1

So it is true that 1 = 0.9999.!

Quote from: paper
0.999  ... a non-finite number
The paper gets this wrong.
0.9999... is greater than 0, and less than 2 (both of them are finite), so it is definitely finite!

Quote from: paper
1 number (2) +1 number (2) =1 number (4) .... therefore 1+1=1
The paper is also confused here.
- It does not attempt to count the numbers, since there are an infinite number of ways you can add up numbers to achieve a certain total

Quote
if a theory is inconsistent it will contain every sentence of the language
A better expression expression would be to refer to Godel's incompleteness theorem, which can be summarised as "A sufficiently complex system will either be incomplete, or it will be inconsistent".
https://en.wikipedia.org/wiki/G%C3%B6del%27s_incompleteness_theorems

There is little debate that science and mathematics are incomplete. Some parts also seem inconsistent, but attempts are made to avoid and or clarify these inconsistencies.

Politics and sociology are also incomplete and often inconsistent...

Quote
So with each opponents view being valid so there is no need/point to argue anymore
I argue that the paper as presented is inconsistent...
Title: Re: Mathematics proven inconsistent an integer= a non-integer
Post by: guest4091 on 12/01/2019 19:34:57
If u=.999...9 for k positions,

then 1-u=.000...1 for k positions.

There is always a remainder >0.

Define u=( (1/10)n, for n=1 to ∞.

The limit of u=1,

meaning u gets closer to the value 1 as n increases without limit.

The limit is an unapproachable boundary which is why u cannot be expressed as an equality.

If u=1 when n=k, the limit statement becomes false.

The repeating sequence of 9's is equated to 1 by rounding the expression, considering the remainder insignificant. This is not a flaw in math concepts, just relaxing the rules for the purpose of approximation.
Title: Re: Mathematics proven inconsistent an integer= a non-integer
Post by: Bored chemist on 12/01/2019 19:44:43
10 times 0.999... is 9.999....
and 10 times 0.999 - 0.999 is  9 times 0.999...
And 9.999... -0.999.... = 9

So 9 times 0.999... is 9
so 0.999... is 9/9
since 9/9 is 1
So 0.999... is 1
Title: Re: Mathematics proven inconsistent an integer= a non-integer
Post by: guest4091 on 15/01/2019 19:55:27
Wiki will provide a good definition of a 'limit".
u=.999... or 9R
1-(.999) =(.001)
1-(.999...........9) = (.000..........1)
By definition all positions in u are 9's.
The difference d=(1-u) is always a positive number 1/10n at position n.
10u-u = 10-10d = 9-9d<1.
Another simple example is x = 1/n.
The limit of x is 0, but x never equals 0.
In your line 1, you multiply the approximation by 10, but not the small difference d.
Title: Re: Mathematics proven inconsistent an integer= a non-integer
Post by: Bored chemist on 15/01/2019 20:03:51
What is 9.9 - 0.9 ?
What is the difference between the number of nines after the decimal point in both cases?
And 9.99 - 0.99?
Title: Re: Mathematics proven inconsistent an integer= a non-integer
Post by: nilak on 21/01/2019 13:25:20
0.(9) seems to be a number within the interval (0,1) but not in (0,1]
whereas 1 can be found in (0,1] and not in (0,1)

Does it still mean 0.(9)=1 ?
Title: Re: Mathematics proven inconsistent an integer= a non-integer
Post by: Bored chemist on 21/01/2019 19:05:01
0.(9) seems ...
To whom, and why?
Title: Re: Mathematics proven inconsistent an integer= a non-integer
Post by: nilak on 22/01/2019 05:51:06
0.(9) seems ...
To whom, and why?
To me.
...because, I thought that 0.999... never reaches 1. But you are right, 0.(9) doesn't clearly mean it belongs to (0,1) and not to (0,1].
Another thing, 1/3 is said to be 0.(3), but is it? What if it is again, belonging to (0,1/3) rather than to (0,1/3]?
Title: Re: Mathematics proven inconsistent an integer= a non-integer
Post by: Bored chemist on 22/01/2019 07:24:58
0.999999...
is the same as 1
it's just 2 ways of writing the same number
Title: Re: Mathematics proven inconsistent an integer= a non-integer
Post by: nilak on 22/01/2019 10:56:16
0.999999...
is the same as 1
it's just 2 ways of writing the same number
Yes, it may be but your explanation is flawed because of circular reference.
You assume 9.999... is 10x0.999... But you need to demonstrate it first.
9.99999x10=99.99990 not 9.99999 so what happens if we go on with bigger and bigger numbers? You will always have that 0 decimal, you can't get rid of it although the difference between the two numbers is smaller and smaller.
Title: Re: Mathematics proven inconsistent an integer= a non-integer
Post by: Bored chemist on 22/01/2019 20:18:40
You assume 9.999... is 10x0.999... But you need to demonstrate it first.
I don't think I need to show that you can multiply a number by 10 by moving the decimal point one place to the right.

And I understand your point, but perhaps you might go back and answer my earlier questions; especially this one
What is the difference between the number of nines after the decimal point in both cases?
Title: Re: Mathematics proven inconsistent an integer= a non-integer
Post by: nilak on 23/01/2019 00:06:15
You assume 9.999... is 10x0.999... But you need to demonstrate it first.
I don't think I need to show that you can multiply a number by 10 by moving the decimal point one place to the right.

And I understand your point, but perhaps you might go back and answer my earlier questions; especially this one
What is the difference between the number of nines after the decimal point in both cases?

By multiplying by 10 you move the decimal point to the right, but in this case you get a number that is written the same way, 9.999...
What is the difference between the number of nines?
The difference is always 1 for any finite number of decimals, but I cannot tell for an infinite number. Does it vanish?
Title: Re: Mathematics proven inconsistent an integer= a non-integer
Post by: Bored chemist on 23/01/2019 07:26:39
How many nines are there after the decimal point in 0.9999....
How many nines are there after the decimal point in 9.9999....
What is the difference between those two numbers?
Title: Re: Mathematics proven inconsistent an integer= a non-integer
Post by: nilak on 23/01/2019 09:58:57
I don't know. ∞-∞ undetermined.
Title: Re: Mathematics proven inconsistent an integer= a non-integer
Post by: guest4091 on 23/01/2019 17:34:35
How many nines are there after the decimal point in 0.9999....
How many nines are there after the decimal point in 9.9999....
What is the difference between those two numbers?
You and like minded viewers are looking at the example with the preconceived notion that .999...equals 1. Any mathematical manipulation will then produce the desired result, supporting your interpretation.
but,
[9+(1-d)] - (1-d) =9. with d=1/10^n, the remainder that is always>0.
If you read the wiki article on 'limits', you should understand.
Title: Re: Mathematics proven inconsistent an integer= a non-integer
Post by: alancalverd on 23/01/2019 17:57:13
0.9999.... however it is signified, means "not quite 1.0" so it can't even be numerically equivalent to 1, let alone an integer.
Title: Re: Mathematics proven inconsistent an integer= a non-integer
Post by: Bored chemist on 23/01/2019 20:20:25
0.9999.... however it is signified, means "not quite 1.0" so it can't even be numerically equivalent to 1, let alone an integer.

I don't know. ∞-∞ undetermined.
It's precisely the same thing on either side of the  "-" sign.
And the difference between two identical things is zero.

What is the difference between the number of nines?
Zero- as I just pointed out.
You and like minded viewers are looking at the example with the preconceived notion that .999...equals 1.
No, I'm not assuming it at all.
I'm showing it.
If you read the wiki article on 'limits', you should understand.
OK, let's look at limits.
What's the limit of the sum of 9 x 10^-n where n ranges from 1 to infinity?

Well, it's clearly 9 times
0.111111111...
which is  the sum of 0.1 +0.01 +0.001... and so on (in the limit)
And that's the sum of a geometric progression
http://mathematics.laerd.com/maths/geometric-progression-intro.php

with a common ratio of 10
And that sum is 1/(10-1)
which is 1/9
So the original number i.e. 0.9999... must be 9/9 which is 1.

Title: Re: Mathematics proven inconsistent an integer= a non-integer
Post by: chiralSPO on 23/01/2019 22:01:13
0.9999.... is equal to exactly 1.

There are many ways of proving this using generally accepted and previously established methods, either algebraically or using limits. If you want to reinvent mathematics such that this is not the case, you may well find that your version of math gives paradoxical or nonsensical answers. (there are still some holes in our system, but overall it works pretty well, and this is not one of those holes--if you really want to tug at the very fiber of our system, look at the "axiom of choice" and the "continuum hypothesis.")

I would urge caution for those who have difficulty interpreting numbers that cannot be expressed perfectly decimal notation. Beware of irrational numbers (which cannot be expressed perfectly as a ratio of any two whole numbers), and especially of transcendental numbers (which cannot be expressed perfectly as a polynomial combination of rational numbers). These numbers are all very much real, easily defined (most of 'em), useful (some of 'em), and together vastly outnumber the "well-behaved" numbers...
Title: Re: Mathematics proven inconsistent an integer= a non-integer
Post by: guest4091 on 24/01/2019 18:01:22
u =.1 + .01 + .001 +...+1/10^n

10u = 1 + u  1/10^n

9u = 1   1/10^n

u = 1/9  (1/10^n)/9

An 'infinite' sequence is never complete since 'infinity' is not a number.
Why did the early mathematicians define a 'limit' instead of declaring an equality?
Title: Re: Mathematics proven inconsistent an integer= a non-integer
Post by: Bored chemist on 24/01/2019 20:02:09
An 'infinite' sequence is never complete
Then 0.9999.... does not exist and we don't need to worry about it.
So, you can stop now.