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A couple of mathematical curiosities

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A couple of mathematical curiosities

You know how 1/3 = 0.33333......(repeating).

I can notate a repeating decimal for the purposes of this venue as 1/3 = .(3) .

Parentheses (x) denote x is repeated incessantly.

Now multiply both sides of the equation by 3:

3 times 1/3 = 3 times .(3)
ergo,
1 = .(9)

Or: One is zero point nine, nine, nine, nine, nine, repeated incessantly.

There have been TONS of debates across the internet with people trying to disprove this equation, 1 = .(9). They seem unequal, and the guess people make is that .(9) is less than 1.
Pages and pages of debate.

Next time we'll take a look at the Banach Tarski theorem which states that you can take a solid sphere of volume 1, cut it into 5 discrete pieces, and rearrange those pieces into two solid spheres of volume 1.
"it is easy to grow crazy"

at1with0

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Re: A couple of mathematical curiosities

You are a math major, I'm sure there must be rules about rounding numbers, that make these kind of odd situations appear logical. By that logic Pi carried out in decimals never ends either, so does than mean we can never determain the circumference of a circle? Does it mean any circumference is not an exact length, if the multiplier never has an ending decimal. How does that affect the rule, the shortest distance between 2 points is a staight line, if you unwrap a circumference into a straight line, but have already determained that circumference is not accuate to begin with, because of Pi? Does that mean we also can not measure the exact length of any straight line?
greeney2

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Re: A couple of mathematical curiosities

greeney2 wrote:You are a math major, I'm sure there must be rules about rounding numbers, that make these kind of odd situations appear logical. By that logic Pi carried out in decimals never ends either, so does than mean we can never determain the circumference of a circle? Does it mean any circumference is not an exact length, if the multiplier never has an ending decimal. How does that affect the rule, the shortest distance between 2 points is a staight line, if you unwrap a circumference into a straight line, but have already determained that circumference is not accuate to begin with, because of Pi? Does that mean we also can not measure the exact length of any straight line?

1=.(9) is no stranger in my opinion than 1=15/15 or 1 = 2 - 1. They are just different ways to write 1.

Every number that has a decimal expansion who terminates has a second form that ends with all 9's.
For example,one half is also equal to 0.4(9)
A transcendental number like pi doesn't have a decimal expansion that terminates, so it is an exception.

Another oddity just occurred to me: since the set of real numbers is uncountable and the set of all descriptions is countable, "most" real numbers do not have a description yet the set of all real numbers can be described. Hmm, that might help actually.

Before I continue, do you mean the idealized concepts of circle, circumference, and lines?
"it is easy to grow crazy"

at1with0

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Re: A couple of mathematical curiosities

Nine is my favorite number
I'm no math genius but I noticed how cool it was when studying numerology way back..though it was my favorite number before I knew that..but once I saw how cool it was..it seriously became my favorite number

it's critical mass..it's event horizon..or, actually that moment just before
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

bionic

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Re: A couple of mathematical curiosities

0, 1, and infinity (aleph null, say) are my favorite numbers.
"it is easy to grow crazy"

at1with0

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Re: A couple of mathematical curiosities

at1with0 wrote:0, 1, and infinity (aleph null, say) are my favorite numbers.

hence, the sig..
nothingness..some kinda something...everything
I get it
and then we get back to your fascination with lines of demarcation, et all, right?
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

bionic

Posts: 9889
Joined: Thu Apr 09, 2009 11:54 am

Re: A couple of mathematical curiosities

bionic wrote:and then we get back to your fascination with lines of demarcation, et all, right?

What do you mean?
"it is easy to grow crazy"

at1with0

Posts: 9183
Joined: Thu Apr 09, 2009 5:55 pm
Location: the coproduct of the amalgam of all structures

Re: A couple of mathematical curiosities

I refuse to explain myself
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

bionic

Posts: 9889
Joined: Thu Apr 09, 2009 11:54 am

Re: A couple of mathematical curiosities

bionic wrote:I refuse to explain myself

I've noticed.
"it is easy to grow crazy"

at1with0

Posts: 9183
Joined: Thu Apr 09, 2009 5:55 pm
Location: the coproduct of the amalgam of all structures

Re: A couple of mathematical curiosities

at1with0 wrote:You know how 1/3 = 0.33333......(repeating).

I can notate a repeating decimal for the purposes of this venue as 1/3 = .(3) .

Parentheses (x) denote x is repeated incessantly.

Now multiply both sides of the equation by 3:

3 times 1/3 = 3 times .(3)
ergo,
1 = .(9)

Or: One is zero point nine, nine, nine, nine, nine, repeated incessantly.

There have been TONS of debates across the internet with people trying to disprove this equation, 1 = .(9). They seem unequal, and the guess people make is that .(9) is less than 1.
Pages and pages of debate.

Next time we'll take a look at the Banach Tarski theorem which states that you can take a solid sphere of volume 1, cut it into 5 discrete pieces, and rearrange those pieces into two solid spheres of volume 1.

1 cannot equal .(9) because you know for a fact that even if .(9) is carried on infinitely, it can never possibly reach 1.

Here we are back to infinity, staring it in the face, because (it's a long story) we exist in a hologram that simply cannot translate perfectly. .(9) can inch closer and closer to 1 until the end of time, and never get there. The same goes for the distance between any 2 points. The same goes for points themselves, which can't possibly physically exist. No point can be demonstrated physically without encompassing multiple points. So points on graphs, and stuff like this, is stuff that can only be imagined. Holographic, man!
Every one who is seriously involved in the pursuit of science becomes convinced that a spirit is manifest in the laws of the Universe-a spirit vastly superior to that of man. - Albert Einstein

frrostedman

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