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A couple of mathematical curiosities

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Postby at1with0 » Thu Jun 23, 2011 9:21 pm

Does 1/3 also imply endless time?

.(3) is a quite full description of 1/3.
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Postby at1with0 » Thu Jun 23, 2011 9:23 pm

It's kind of an interesting phenomena. I say I know 1=.(9) and you aren't placing much faith in my word or the word of countless books and articles on the subject that I could point you in the direction in.

Seems like a familiar scenario.
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Postby bionic » Fri Jun 24, 2011 1:18 am

Did you guys see the latest, "Through the Wormhole"?
It was all about time.
I have to wathc it again, as it boggled my mind.
Too much fricken math!!
http://science.discovery.com/tv/through-the-wormhole/
basically, all time is happening now..I got that much
some pople think time doesn't really exist..it's an illusion to do with our reality filters
but some people feel it's really real, too
there's a debate going on
:shock:
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What is this Wonka, some kind of funhouse?
Why? Are you having fun?
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Postby at1with0 » Fri Jun 24, 2011 12:26 pm

Haven't seen it . Is it good?

This is for frrosty or anyone who is willing to give it a more thorough treatment:

http://en.wikipedia.org/wiki/0.999...
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Postby bionic » Fri Jun 24, 2011 7:29 pm

it made me realize that only someone that really gets math could maybe, have the software in their brain to be able to grasp whatever it takes to make that paradigm shift needed to overcome the illusion of time.
So it was good in that way.
Willie Wonka quotes..
What is this Wonka, some kind of funhouse?
Why? Are you having fun?
A little nonsense now and then is relished by the wisest men.
We are the music makers, we are the dreamers of dreams
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Postby at1with0 » Fri Jun 24, 2011 7:54 pm

bionic wrote:it made me realize that only someone that really gets math could maybe, have the software in their brain to be able to grasp whatever it takes to make that paradigm shift needed to overcome the illusion of time.
So it was good in that way.

I saw the 2 minute shortie that was in the link. Looked interesting but I didn't follow how variations in the speed of light in distant parts of the universe affected the conclusion that time is or isn't an illusion.

If uncertainty were not involved, one could make a list (ie set) of all positions and times at those positions of all particles and that list would be a static description of something that is dynamic. The static totality would be outside time in a sense in that it never changes yet describes change.

Right or wrong, I think that at least makes it conceivable that the illusion of time can be "overcome" for want of a different word.
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Postby greeney2 » Fri Jun 24, 2011 9:23 pm

I found this, related to rounding rules. Maybe as a math major you could explain where these rounding rules came from and how they were accepted to be a valid mathmatical rule? Obvious, they were adopted becasue of delemia's like you discribe 1=.9 example. These rules must come into play converting from fractions to decimals, a division process, but multiplying to proove your answer does not work? It produces a delemia like the 1=.9, until you follow the accepted rules of rounding, than it comes out right. Somewhere mathmatics discovered these things happen, converting whole numbers or fractions into decimals. In robotics we controled machine accuracy with encoders that counted inches of travel with very high counting numbers. the more numbers you divided up a 1 inch increment, the closer you could return to the same position. This was called resolution per inch. Decimals allow us to count in very high resolution in parts of whole numbers. Fractions at best are very low resolution and reduced to very crude approximations. You know when you are about about half way walking home from school. But if you knew school is 4834 steps from home half way is 2417 steps. Using fractions your resolution is a few larger segments, rather than many many small segments. 1=.9 if you are using 1/3 as the fraction. 1=1 if you use 1/4 as the fraction becasue it will end in a zero.

When rounding whole numbers there are two rules to remember:
I will use the term rounding digit - which means: When asked to round to the closest tens - your rounding digit is the second number to the left (ten's place) when working with whole numbers. When asked to round to the nearest hundred, the third place from the left is the rounding digit (hundreds place).

Rule One. Determine what your rounding digit is and look to the right side of it. If the digit is 0, 1, 2, 3, or 4 do not change the rounding digit. All digits that are on the right hand side of the requested rounding digit will become 0.

Rule Two. Determine what your rounding digit is and look to the right of it. If the digit is 5, 6, 7, 8, or 9, your rounding digit rounds up by one number. All digits that are on the right hand side of the requested rounding digit will become 0.

Rounding with decimals: When rounding numbers involving decimals, there are 2 rules to remember:

Rule One Determine what your rounding digit is and look to the right side of it. If that digit is 4, 3, 2, or 1, simply drop all digits to the right of it.

Rule Two Determine what your rounding digit is and look to the right side of it. If that digit is 5, 6, 7, 8, or 9 add one to the rounding digit and drop all digits to the right of it.

Rule Three: Some teachers prefer this method:

This rule provides more accuracy and is sometimes referred to as the 'Banker's Rule'. When the first digit dropped is 5 and there are no digits following or the digits following are zeros, make the preceding digit even (i.e. round off to the nearest even digit). E.g., 2.315 and 2.325 are both 2.32 when rounded off to the nearest hundredth. Note: The rationale for the third rule is that approximately half of the time the number will be rounded up and the other half of the time it will be rounded down.

An example:

765.3682 becomes:

1000 when asked to round to the nearest thousand (1000)

800 when asked to round to the nearest hundred (100)

770 when asked to round to the nearest ten (10)

765 when asked to round to the nearest one (1)

765.4 when asked to round to the nearest tenth (10th)

765.37 when asked to round to the nearest hundredth (100th.)

765.368 when asked to round to the nearest thousandth (1000th)
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Postby at1with0 » Fri Jun 24, 2011 9:44 pm

Actually, 1=.(9) is not a dilemma but a curiosity or fact or whatever.
Rounding is 100% a convention at integer multiples of 1/2 you say round up but you could round down. Kind of like how the order of operations in algebra (parentheses, exponents, multiplication, division, addition, subtraction) is 100% a convention.

What exactly .(9) is will reveal why it is equal to one. In the wiki article, it explains the Cauchy construction of the real numbers.

The number 1 has a few definitions which are equivalent but I would use the Cauchy definition when comparing it to .(9).

When I say 3 and 4 are different, they have a definite difference, 1. Or 5 and 11. The difference is 6.

x = y if and only if the difference between x and y is zero.

x < y if and only if y - x > 0. In engrish, x is less than y if and only if the difference is positive (greater than zero).

The difference between two numbers is not something that changes over time.

The hypothesis .(9) < 1 can be tested. .(9) is less than 1 if and only if 1 - .(9) is positive.
Let x=.(9) for simpler notation.
Some facts:
x > .9
Ok?

Also,
x>.99
and
x>.999
and x>.9999
and x>.99999
etc.

Now that means that all of the following hold:
1-x < .1 (ie the difference is less than .1)
1-x < .01 (ie the difference is less than .01)
1-x < .001 (ie the difference is less than .001)
1-x < .0001 (ie the difference is less than .0001)

etc.

That means the number 1-x has the property that it is smaller than all positive real numbers.
Also, 1-x being the difference of two real numbers is itself a real number. Clearly, 1-x is not negative.

The only real number that (A) is smaller than all positive numbers and (B) is not negative is ZERO.
IOW, 1-x = 0. Ergo, 1=x. Recall that x was .(9) so 1 = .(9).

QED



And keep in mind that I'm not referring to how .9=1 here. .(9) is completely different from .9.
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Postby greeney2 » Fri Jun 24, 2011 10:12 pm

Its beyond my level of math, is the best way I can say it. If I do the rounding by the rules for .9999, I'm back to 1.0 again.
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Postby at1with0 » Fri Jun 24, 2011 10:33 pm

.9999 is definitely different from 1.

.(9) is equal to 1.

;)
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