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ryan93
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09 Feb 2011, 8:05 am

Orwell wrote:
ryan93 wrote:
Makes sense, I have "God Created the Integers" sitting on my shelf, so I'll see if I can make it past Boole and move of to Cantor.

I have not read that book, but I instinctively distrust anything which attempts to popularize a detailed and technical subject. You would likely be better educated (but far worse entertained) by a textbook. Topology by Munkres has a pretty decent treatment of these concepts.

soulecho wrote:
And to make it even more confusing, the set of numbers on the interval [0,1] has the exact same cardinality as R.

And the set of numbers which lie on the unit circle (x^2+y^2=1) has greater cardinality than the entire real line.


The book is a collection of papers written by the famous mathematicians; Euclid, Leibniz, Boole, Godel and a load of others. It's extremely technical, I even found stuff as early as Leibniz to be challenging :) Math textbooks never did really taught me anything, as if I can't visualise a mathematical process I'm not very proficient at it. That's why I love Linear Algebra so much :)


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b9
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09 Feb 2011, 8:15 am

infinity is not a quantity.

there are an infinite amount of points in a line that is infinitessimally short.
and there is likewise an infinite amount of points in a line that is infinitely long.

infinity does not equal infinity. infinity is not a quantity.



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09 Feb 2011, 8:49 am

ryan93 wrote:
The book is a collection of papers written by the famous mathematicians; Euclid, Leibniz, Boole, Godel and a load of others. It's extremely technical, I even found stuff as early as Leibniz to be challenging :)

OK, that does sound very interesting.


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ryan93
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09 Feb 2011, 9:41 am

Orwell wrote:
ryan93 wrote:
The book is a collection of papers written by the famous mathematicians; Euclid, Leibniz, Boole, Godel and a load of others. It's extremely technical, I even found stuff as early as Leibniz to be challenging :)

OK, that does sound very interesting.


It's a great book, here's the list of mathematicians covered. A very good selection, in my opinion :)

Euclid
Archimedes
Diophantus
René Descartes
Isaac Newton
Pierre-Simon Laplace
Joseph Fourier
Carl Friedrich Gauss
Augustin-Louis Cauchy
George Boole
Bernhard Riemann
Karl Weierstrass
Richard Dedekind
Georg Cantor
Henri Lebesgue
Kurt Gödel
Alan Turing


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ruveyn
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09 Feb 2011, 10:19 am

b9 wrote:
infinity is not a quantity.

.


Infinity can be a cardinal and it can be an ordinal. So it is a quantity. However it does not obey the same algebraic laws that finite quantities do.

ruveyn



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09 Feb 2011, 11:36 am

ryan93 wrote:
It's a great book, here's the list of mathematicians covered. A very good selection, in my opinion :)

Euclid
Archimedes
Diophantus
René Descartes
Isaac Newton
Pierre-Simon Laplace
Joseph Fourier
Carl Friedrich Gauss
Augustin-Louis Cauchy
George Boole
Bernhard Riemann
Karl Weierstrass
Richard Dedekind
Georg Cantor
Henri Lebesgue
Kurt Gödel
Alan Turing

Add some Abel, Poincare, and Mandelbrot and I like it.


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ryan93
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09 Feb 2011, 11:52 am

Orwell wrote:
ryan93 wrote:
It's a great book, here's the list of mathematicians covered. A very good selection, in my opinion :)

Euclid
Archimedes
Diophantus
René Descartes
Isaac Newton
Pierre-Simon Laplace
Joseph Fourier
Carl Friedrich Gauss
Augustin-Louis Cauchy
George Boole
Bernhard Riemann
Karl Weierstrass
Richard Dedekind
Georg Cantor
Henri Lebesgue
Kurt Gödel
Alan Turing

Add some Abel, Poincare, and Mandelbrot and I like it.


No mandelbrot, suprisingly :?


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b9
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10 Feb 2011, 8:25 am

ruveyn wrote:
b9 wrote:
infinity is not a quantity.

.


Infinity can be a cardinal and it can be an ordinal. So it is a quantity. However it does not obey the same algebraic laws that finite quantities do.

ruveyn


all "quantities" are definitions of finite amounts. infinity is not a finite amount and so the definition if infinity can never be final, and thus there can be no complete definition of infinity.

infinity is as indefinite as zero.

both of them are external to existence.

it is better to speculate with your mind than to use a search engine to find what others think.

you and no one else can not quantify infinity, and i will not waste time reading any attempts to do so.

the very definition of the word means "never ending", so no end can be arrived at in speculation about it.

i am so tired and tammy is yelling for me to come to bed.



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10 Feb 2011, 10:00 am

b9 wrote:

infinity is as indefinite as zero.

.


Zero is very definite. It is the identity element (thus it is unique) of an additive group.

Arithmetically it is what you get when you subtract a quantity from itself.

ruveyn



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11 Feb 2011, 5:37 am

b9 wrote:

all "quantities" are definitions of finite amounts.


No. Only in your restricted view of what a "quantity" can be.

b9 wrote:
infinity is not a finite amount


Infinity is not an "amount", it's a property of certain sets of elements. And it can indeed be defined completely.

b9 wrote:
and so the definition if infinity can never be final, and thus there can be no complete definition of infinity.


Wrong. There is a mathematical definition of infinity (of various kinds of infinity), and it is final.

b9 wrote:
infinity is as indefinite as zero.


As ruveyn wrote, zero has very much a definition.

b9 wrote:
both of them are external to existence.


What does this even mean?

b9 wrote:
it is better to speculate with your mind than to use a search engine to find what others think.


It was a question about maths, not about speculating about a goody-feely idea of what "infinity" is. Maths is a science. It's not about what you think. It's about what is.

b9 wrote:
you and no one else can not quantify infinity, and i will not waste time reading any attempts to do so.


Your loss. Refusing knowledge because it doesn't fit your preconceptions has a name: bigotry. Your anti-science rant is noted.

b9 wrote:
the very definition of the word means "never ending", so no end can be arrived at in speculation about it.


Etymology and definition are different things. Folk use and scientific use of a word are two different things. This thread is in the "Computer, Math, Science and Technology" subforum. It's about the mathematical notion of infinity, not the flat everyday one. Your rant is ineffective because you are not talking about the same thing that we are talking about. If you want to discuss the mathematical notion of infinity, you are welcome to do so here. If you do not know enough about the mathematical notion of infinity, you are welcome to ask questions about it. But do not insult our intelligence with half-baked rants about things that have nothing to do with the subject at hand. And do not insult scientists when you have no idea what they are talking about.