[spycosis]

Here is an equation that grabbed my attention many years ago,

10χ - χ = 9χ This is an absolute truth
just as 10-1 = 9

However if we assign χ with the value 0.999̇̅
and perform the operation, something strange happens.

χ = 0.999̅

⇒10χ = 10 x 0.999̅ = 9.999̅

⇒ 10χ - χ = 9.999̅ - 0.999̅ = 9.000

⇒ 9χ = 9

⇒ χ = 1


Apparently, the impossible has taken place. The value of x can never change during a mathematical operation , but here it apparently does. For me, the equation transcends mathematics, and has become something I study more on a philosophical level.

I have debated this subject with maths tutors, graduates and students, and there is no solid, infallible answer as to why this takes place. I have my theories, though they conflict each other.

I am more interested to hear what the DR members' theories are.

What do you think ?

[deanmine]

if in observation of "matter" the effect of observation effects its "state" (collapse of the wave function)

its been argued in math as to weather or not math is physical or only theoretical. if these two properties of math "collide" where the act of "measuring" .999... can equal 1.00... seems like the act of math can enrich the system of numbers.

I HAVE NO CLUE I HATE FUCKIN MATH

[NEVERBACKZ]

I have the answer to this. Somewhere.

[jinhwangtikatang]

You state :-

⇒10χ = 10 x 0.999̅ = 9.999̅

This is incorrect, 10x 0.999 is not 9.999, it is 9.990.

therefore 9.990 - 0.999 = 8.991

8.991 / 9 = 0.999

[jinhwangtikatang]

Had some more thoughts on this overnight.
You may well have X as a recurring number, if so I didn't recognise the line symbol after the nine as denoting that, so I'll explain why that wouldn't effect my previous solution.

My Previous example was

X=0.999
Therefore 10X (10 times X )= 9.990.
Therefore 9.990 - 0.999 = 8.991
Therefore 8.991 / 9 = 0.999

If we used your figures instead of mine, and take 10X as 9.999, then the figure we take as 10 times X is actually (x times 10) + 0.009 )
This means that when we remove 1 times X and then divide by 9, the actual figure we are left with is X + (0.009/9) which is x+(0.001) which is the reason for the discrepancy of the same amount (0.001).
In fact we are Multipying X initially by very slightly MORE than 10, which is why we have the discrepancy.

Even if X is a recurring number, it doesn't matter, we can extend the same formula ad infinitum, so for example if we extend X by 1 decimal point we get :-

X=0.9999
⇒10χ = 10 x 0.9999 = 9.9990
Therefore 9.9990 - 0.9999 = 8.9991
Therefore 8.9991/9 = 0.9999

if we were to use your method of calculation with the 4 digit example I've just given, then we get

X=0.9999
X Times 10 = 9.9999
9.9999 - 0.9999 = 9
9x = 9
x=1

We can take this to as many decimal places as you like, and it doesn't matter, the discrepancy is caused by a miscalculating 10X as (10 times X)+ An amount, which varies depending on how many decimal places you have taken the calculation to.
The more decimal places we take the calculation to, the smaller the discrepancy is, but its always there.

[deanmine]

so ur saying the answer is ....... PIE

[spudigitti]

111,111,111 ×111,111,111...????

[spycosis]

Originally Posted by jinhwangtikatang ↗

Had some more thoughts on this overnight.
You may well have X as a recurring number, if so I didn't recognise the line symbol after the nine as denoting that, so I'll explain why that wouldn't effect my previous solution.

My Previous example was

X=0.999
Therefore 10X (10 times X )= 9.990.
Therefore 9.990 - 0.999 = 8.991
Therefore 8.991 / 9 = 0.999

If we used your figures instead of mine, and take 10X as 9.999, then the figure we take as 10 times X is actually (x times 10) + 0.009 )
This means that when we remove 1 times X and then divide by 9, the actual figure we are left with is X + (0.009/9) which is x+(0.001) which is the reason for the discrepancy of the same amount (0.001).
In fact we are Multipying X initially by very slightly MORE than 10, which is why we have the discrepancy.

Even if X is a recurring number, it doesn't matter, we can extend the same formula ad infinitum, so for example if we extend X by 1 decimal point we get :-

X=0.9999
⇒10χ = 10 x 0.9999 = 9.9990
Therefore 9.9990 - 0.9999 = 8.9991
Therefore 8.9991/9 = 0.9999

if we were to use your method of calculation with the 4 digit example I've just given, then we get

X=0.9999
X Times 10 = 9.9999
9.9999 - 0.9999 = 9
9x = 9
x=1

We can take this to as many decimal places as you like, and it doesn't matter, the discrepancy is caused by a miscalculating 10X as (10 times X)+ An amount, which varies depending on how many decimal places you have taken the calculation to.
The more decimal places we take the calculation to, the smaller the discrepancy is, but its always there.

Now we are following the track of a zero existing at the end of infinity, I am deeply curious as to how this number would appear if we could write it so that it extended out from the earth , into space forever. And ended with a zero. Where would the zero be ? Not in our physical universe. But then you could say that mathematical operations that take place outside this universe have a direct influence on the mathematics of the space in which we live, and vice versa. That's what I think is going on here, the crossing of boundaries, or rather a demonstration that it is possible.

[deanmine]

string.....

[jinhwangtikatang]

Originally Posted by spycosis ↗

Now we are following the track of a zero existing at the end of infinity, I am deeply curious as to how this number would appear if we could write it so that it extended out from the earth , into space forever. And ended with a zero. Where would the zero be ? Not in our physical universe. But then you could say that mathematical operations that take place outside this universe have a direct influence on the mathematics of the space in which we live, and vice versa. That's what I think is going on here, the crossing of boundaries, or rather a demonstration that it is possible.

Ah, infinity ! That leads me to one of my favourite programmes of all time, I think you'll enjoy it.

http://www.dailymotion.com/video/x1k...pdtv-xvid_tech