The lie of algebra
The lie of algebra
1/3 is a symbol for a set of 4 words, it is not a NUMBER.
Only a single number CAN POSSIBLY = 1. Other numbers may ADD UP to 1, but they don't EQUAL 1. Since 1 clearly = 1, .99999 repeating simply cannot equal 1.
.33(repeting) is irrational.
.99999 does not equal 1. It might in the CURRENT UNDERSTANDING of mathematics, but that don't make it true.
Mathematics cannot even prove that .99999 ... is not equal to 1.
Right now, math really can't deal with infinite numbers
.9 repeating, an irrational number, is ABSOLUTELY EQUAL to the rational number 1. Can this be used as proof to show there is no such thing as irrational numbers?
I'm half tempted to say there isn't really a right or wrong answer
I think I've come to the conclusion that .999... = 1 in the same sense that .333... = 1/3. Which is to say, it doesn't, quite, but we treat it like it does because our decimal system has problems.
0.9 recurring does not equal 1. Why? Because it's 0.9 recurring.
1 = .9 repeating IF WE WANT IT TO.
so does that make 2.999 mean <3 or =3 ?
it's very irrational and so unattainably specific gah.
Only a single number CAN POSSIBLY = 1. Other numbers may ADD UP to 1, but they don't EQUAL 1. Since 1 clearly = 1, .99999 repeating simply cannot equal 1.
.33(repeting) is irrational.
.99999 does not equal 1. It might in the CURRENT UNDERSTANDING of mathematics, but that don't make it true.
Mathematics cannot even prove that .99999 ... is not equal to 1.
Right now, math really can't deal with infinite numbers
.9 repeating, an irrational number, is ABSOLUTELY EQUAL to the rational number 1. Can this be used as proof to show there is no such thing as irrational numbers?
I'm half tempted to say there isn't really a right or wrong answer
I think I've come to the conclusion that .999... = 1 in the same sense that .333... = 1/3. Which is to say, it doesn't, quite, but we treat it like it does because our decimal system has problems.
0.9 recurring does not equal 1. Why? Because it's 0.9 recurring.
1 = .9 repeating IF WE WANT IT TO.
so does that make 2.999 mean <3 or =3 ?
it's very irrational and so unattainably specific gah.
wet, dirty and dangerous.
Re: The lie of algebra
I feel lost but I very much like this.
only when the clock stops does time come to life
Re: The lie of algebra
it's a love note see last year's
a little less complex
but here's another interesting thing:
1= 1/2 + log2Hav > formula for calculating Tsunami intensity
The first scale that genuinely calculated a magnitude for a tsunami, rather than an intensity at a particular location was the ML scale proposed by Murty & Loomis based on the potential energy. Difficulties in calculating the potential energy of the tsunami mean that this scale is rarely used. Abe introduced the tsunami magnitude scale Mt, calculated from,
Mt= a log h + b log R =D
where h is the maximum tsunamiwave amplitude (in m) measured by a tide gauge at a distance R from the epicenter, a, b & D are constants used to make the Mt scale match as closely as possible with the moment magnitude scale.
a little less complex
but here's another interesting thing:
1= 1/2 + log2Hav > formula for calculating Tsunami intensity
The first scale that genuinely calculated a magnitude for a tsunami, rather than an intensity at a particular location was the ML scale proposed by Murty & Loomis based on the potential energy. Difficulties in calculating the potential energy of the tsunami mean that this scale is rarely used. Abe introduced the tsunami magnitude scale Mt, calculated from,
Mt= a log h + b log R =D
where h is the maximum tsunamiwave amplitude (in m) measured by a tide gauge at a distance R from the epicenter, a, b & D are constants used to make the Mt scale match as closely as possible with the moment magnitude scale.
wet, dirty and dangerous.
Re: The lie of algebra
I'm not good enough at maths to argue all these points as accurately as I should, but I'd heartily recommend David Foster Wallace's "Everything and More: A compact history of infinity" (http://books.google.co.uk/books/about/E ... edir_esc=y) which'll do the job much better than I can. The short of it is, no, contemporary maths has pretty much got its head round infinity, although it still totally messes with the human mind. Some of the problems you talk about (all of which are rooted in Zeno's paradoxes) got nobbled by Newton, and most of the rest got mopped up by Cantor.
I'm going to give it a bash though. Apologies for the pedantry, and I'm not trying to be patronising; this is just one of my favourite subjects and I like talking about it:
An irrational number will never be equal to a rational number, because they are totally different sets, but complex numbers or even sums and powers and multiplications of irrational numbers can quite happily be rational. See, for example, e^1(pi)=1.
As for "no such thing", well, that depends on whether you think numbers exist or not. Fortunately, the maths works regardless of your philosophical stance on this question.
Actual maths at first glance may seem more boring than exciting and wild philosophical epiphanies, but the excitement lasts much longer.
I'm going to give it a bash though. Apologies for the pedantry, and I'm not trying to be patronising; this is just one of my favourite subjects and I like talking about it:
That's sort of what Pythagoras said about the square root of 2. The way we deal with this now is by talking about different sets of numbers. 1/3 is not a natural number, it's true, but it is a real number. Root2 belongs to the set of irrational numbers.1/3 is a symbol for a set of 4 words, it is not a NUMBER.
This is a tautological argument. Yes, only one numerical value can equal 1. But the two symbols 0.999r and 1 are different symbols for the same numerical value. Bothy = 1.Only a single number CAN POSSIBLY = 1. Other numbers may ADD UP to 1, but they don't EQUAL 1. Since 1 clearly = 1, .99999 repeating simply cannot equal 1.
No, it's a rational number, because it can be represented by 1/3. Irrational numbers are numbers which cannot be represented by a fraction of integers (2, 1, 0, 1, 2 ...), like root2 or pi..33(repeting) is irrational.
Your computer couldn't work without it being true. Also, all the planets would spin out of orbit..99999 does not equal 1. It might in the CURRENT UNDERSTANDING of mathematics, but that don't make it true.
Newton proved that it is (and Leibniz, possible at the same time). That's what calculus is for.Mathematics cannot even prove that .99999 ... is not equal to 1.
Almost all postNewtonian inventions depend on maths learning how to cope with infinities through integration and differentiation; almost all postCantorian inventions depend on learning how to cope with the resultant paradoxes through transfinite numbers. Infinity is at the heart of modern technology.Right now, math really can't deal with infinite numbers
First, 0.999r is not necessarily an irrational number. I can't remember how to prove whether a number is or is not irrational, though some judicious wikipediaing might help. But given that you argued that 0.333r is irrational when in fact it is perfectly rational, you probably want to swot up on what irrational numbers are anyway..9 repeating, an irrational number, is ABSOLUTELY EQUAL to the rational number 1. Can this be used as proof to show there is no such thing as irrational numbers?
I'm half tempted to say there isn't really a right or wrong answer
An irrational number will never be equal to a rational number, because they are totally different sets, but complex numbers or even sums and powers and multiplications of irrational numbers can quite happily be rational. See, for example, e^1(pi)=1.
As for "no such thing", well, that depends on whether you think numbers exist or not. Fortunately, the maths works regardless of your philosophical stance on this question.
Yes, they're the same type of decimal: the ... is important because it indicates that both are an infinite series. 0.999r=1 and 0.333r=1/3 because, after Newton et al, we know how to sum an infinite series.I think I've come to the conclusion that .999... = 1 in the same sense that .333... = 1/3. Which is to say, it doesn't, quite, but we treat it like it does because our decimal system has problems.
You say this because you're not quite sure what an infinite series is. The argument you're making here is exaactly the argument that many of Zeno's paradoxes make. If 0.999r does not equal 1, Achilles can never overtake the tortoise.0.9 recurring does not equal 1. Why? Because it's 0.9 recurring.
See response to "no such thing" above.1 = .9 repeating IF WE WANT IT TO
2.999 is less than 3. But 2.999r or 2.999... = 3. Now I'm actually being pedantic, but it's a useful point: you're conceiving as 2.999... as just 2.999 with lots more 9s. It's not. It's 2. with an infinite number of 9s. Infinity is not a very large number. It's a totally different type of thing.so does that make 2.999 mean <3 or =3 ?
Actual maths at first glance may seem more boring than exciting and wild philosophical epiphanies, but the excitement lasts much longer.
Re: The lie of algebra
I'd have expected you to be more a Tadeus Kantor man
consistency is the hobgoblin of small minds
Re: The lie of algebra
Him too.
(All the Cantors are awesome. Apart from Eric.)
(All the Cantors are awesome. Apart from Eric.)

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Re: The lie of algebra
Think you missed the point a bit Harry...
Mike
Dawnsio 'mlaen i'r gwres prynhawn a rwy'n addo erbyn yfori byddai wedi mynd, hwyl fawr i pawb, hwyl fawr i pawb...
Dawnsio 'mlaen i'r gwres prynhawn a rwy'n addo erbyn yfori byddai wedi mynd, hwyl fawr i pawb, hwyl fawr i pawb...
Re: The lie of algebra
But that maths is unable to comprehend love doesn't mean maths is unable to comprehend maths, and you don't need to argue the former in order to demonstrate the latter.
Or, to put it another way, infinity is one of the things I love and get excited about, so I can't help talking about it if I get the chance.
Or, to put it another way, infinity is one of the things I love and get excited about, so I can't help talking about it if I get the chance.
Re: The lie of algebra
i should have wrote some stuff with last year's valentine then maybe the intended would have responded, and i would have known they read it.
now i know
 To be perfectly honest i just copied and pasted a bunch of maths quotes that related to both the xkcd as well as the semi private joke i have going on which is continued from last year....
i intentionally posted it in technology for the purpose of drawing the attention of someone... though i know it would have been seen regardless, i figured a post in technology, esp. by me, would have drawn more special attention.
so anyway.
yes.
i'm just publicly flaunting a private thing because i'm obnoxious like that.
Happy VD.
xoxxo to all of you and
<3 to 1
now i know
 To be perfectly honest i just copied and pasted a bunch of maths quotes that related to both the xkcd as well as the semi private joke i have going on which is continued from last year....
i intentionally posted it in technology for the purpose of drawing the attention of someone... though i know it would have been seen regardless, i figured a post in technology, esp. by me, would have drawn more special attention.
so anyway.
yes.
i'm just publicly flaunting a private thing because i'm obnoxious like that.
Happy VD.
xoxxo to all of you and
<3 to 1
wet, dirty and dangerous.

 Posts: 1113
 Joined: Sun Nov 23, 2008 10:16 am
 Location: Edinburgh!
 Contact:
Re: The lie of algebra
*holds tongue*HGiles wrote:so I can't help talking about it if I get the chance.
Mike
Dawnsio 'mlaen i'r gwres prynhawn a rwy'n addo erbyn yfori byddai wedi mynd, hwyl fawr i pawb, hwyl fawr i pawb...
Dawnsio 'mlaen i'r gwres prynhawn a rwy'n addo erbyn yfori byddai wedi mynd, hwyl fawr i pawb, hwyl fawr i pawb...
Re: The lie of algebra
*types selfcontradictory action*ChaoticReality wrote:*holds tongue*HGiles wrote:so I can't help talking about it if I get the chance.
Re: The lie of algebra
at least someone's got some loveHGiles wrote: infinity is one of the things I love and get excited about, so I can't help talking about it if I get the chance.
sry ( <3 )mike, harry wins ;pHGiles wrote:*types selfcontradictory action*ChaoticReality wrote:*holds tongue*HGiles wrote:so I can't help talking about it if I get the chance.
wet, dirty and dangerous.
Re: The lie of algebra
I rarely do the whole real life laugh out loud whilst typing LOL but... LOL.HGiles wrote:*types selfcontradictory action*ChaoticReality wrote:*holds tongue*HGiles wrote:so I can't help talking about it if I get the chance.
I love this thread.
only when the clock stops does time come to life
Re: The lie of algebra
I can't do numbers but, here, have some love:
http://www.flickr.com/photos/kipling_we ... /lightbox/
http://www.flickr.com/photos/kipling_we ... /lightbox/
only when the clock stops does time come to life
Re: The lie of algebra
Sounds a lot like the zen maths of Douglas Hofstadter in his book Godel, Escher, Bach. Now there's an afternoon or three's reading.