[mekrob]

$this->bbcode_second_pass_quote('Carlhole', 'h')ttp://zappinternet.com/index.php?video=FuMkVebYot

[PenultimateManStanding]

$this->bbcode_second_pass_quote('Andrew_S', '')$this->bbcode_second_pass_quote('PenultimateManStanding', ' ')Same thing goes for pi: it's a symbol for a number that doesn't exist. It is a very important ratio but it can't be written with numbers.

[PenultimateManStanding]

$this->bbcode_second_pass_quote('mekrob', '')$this->bbcode_second_pass_quote('Carlhole', 'h')ttp://zappinternet.com/index.php?video=FuMkVebYot

[Licho]

Well even 1/3 cannot be written down in decimal fixed point notation so what??

I mean how can you say it doesnt exist. You just cannot represent it using finite number of symbols in one kind of notation. But that doesnt mean anything..

I cannot express how I feel about certain people using words. But that doesnt mean they dont exist

[JustinFrankl]

$this->bbcode_second_pass_quote('mekrob', '')$this->bbcode_second_pass_quote('Carlhole', 'h')ttp://zappinternet.com/index.php?video=FuMkVebYot

[PenultimateManStanding]

$this->bbcode_second_pass_quote('Licho', 'W')ell even 1/3 cannot be written down in decimal fixed point notation so what??

I mean how can you say it doesnt exist. You just cannot represent it using finite number of symbols in one kind of notation. But that doesnt mean anything..

[PenultimateManStanding]

I enjoy thinking about this stuff like Raph enjoys his mythology. It's interesting to me that radical 5 can be constructed geometrically. It turns up in the construction of a pentagon. In that case, though, the unit of measurement and the radical 5 length are incommensurate. The whole business of incommensurate lengths is what threw the Greek mathematicians for a loop when they discovered it. We tend to think more algebraically and more with numbers than geometrically as the Greeks did. So from a geometrical perspective, one can say that radical five is very much a real length, it just doesn't have a common length with 1. But from that it follows that it can't be measured since all measurements are done with units of measurement. And Raph, your friend Isaac Newton was also very adept at geometry.

[PenultimateManStanding]

$this->bbcode_second_pass_quote('JustinFrankl', 'e')dit: nevermind, don't know what I was thinking

[JustinFrankl]

$this->bbcode_second_pass_quote('PenultimateManStanding', '')$this->bbcode_second_pass_quote('JustinFrankl', 'e')dit: nevermind, don't know what I was thinking

[smallpoxgirl]

$this->bbcode_second_pass_quote('JustinFrankl', 'N')atural logarithms are computed with base e, another irrational number. How would you represent e in base e? How would you represent radical 5 in base radical 5 (ignoring the more important question, why would you want to)?

[PenultimateManStanding]

doesn't seem to me that a logarithmic base is the same as a number system base. A number system in base radical 5 doesn't make any sense because the bases have to be whole counting numbers. There's the binary numbers, octal, decimal, hexadecimal, ect. all whole numbers, and one could set up a base 5 system too, but not base radical five. If I wrong, I can't think of how it would be done at the moment.

[JustinFrankl]

$this->bbcode_second_pass_quote('smallpoxgirl', '')$this->bbcode_second_pass_quote('JustinFrankl', 'N')atural logarithms are computed with base e, another irrational number. How would you represent e in base e? How would you represent radical 5 in base radical 5 (ignoring the more important question, why would you want to)?

[PenultimateManStanding]

another way to put it: how does one count using a continuous function?

[smallpoxgirl]

$this->bbcode_second_pass_quote('JustinFrankl', '')$this->bbcode_second_pass_quote('', 'e') in base e is 1. Same for radical 5 in base radical 5

[JustinFrankl]

$this->bbcode_second_pass_quote('PenultimateManStanding', 'd')oesn't seem to me that a logarithmic base is the same as a number system base. A number system in base radical 5 doesn't make any sense because the bases have to be whole counting numbers. There's the binary numbers, octal, decimal, hexadecimal, ect. all whole numbers, and one could set up a base 5 system too, but not base radical five. If I wrong, I can't think of how it would be done at the moment.

[PenultimateManStanding]

$this->bbcode_second_pass_quote('JustinFrankl', ' ')My point was that irrational numbers can be wholly represented by integers. It still isn't necessarily useful.

[JustinFrankl]

$this->bbcode_second_pass_quote('PenultimateManStanding', '')$this->bbcode_second_pass_quote('JustinFrankl', ' ')My point was that irrational numbers can be wholly represented by integers. It still isn't necessarily useful.

[PenultimateManStanding]

$this->bbcode_second_pass_quote('JustinFrankl', '
')But you're right, in order to be useful to most people, a number system would have to be discrete. Irrational bases are probably only of theoretical (i.e., geek) value.

[PenultimateManStanding]

$this->bbcode_second_pass_quote('JustinFrankl', '
')The number system doesn't have to be discrete, it's just that humans have a hard time conceptualizing the world in a continuous manner. The world is continuous, we tend to perceive it discretely. Which makes our accomplishments in mathematics and science all the more remarkable.

[PenultimateManStanding]

There is a problem in mathematics that was apparently resolved by Richard Dedekind; the problem of the "contradiction between the continuous nature of the number line continuum and the discrete nature of the numbers themselves." (from wiki on the Dedekind cut) I took a course in the Foundations Of Mathematics once about 15 years ago where this came up.) I knew the notation for set theory a bit better back then. But I'm still puzzled by this since the theory seems to be that all the irrationals can be placed on a number line in principle and that there are no "gaps". We also covered Cantor's work in that very interesting class and there I learned that rational numbers can be mapped one-to-one onto the integers so that rationals are "countable". But irrationals cannot be counted and they constitute a higher order infinite set. In other words, the rational numbers are like islands in a sea of irrationals. It would seem to me that most of these irrational numbers have no name or expression, that they exist only in principle and we could never hope to even begin to know them and their properties except for a very few such as roots and pi and euler's number, etc.

once again, I fail to see how any number system could use an irrational base since number systems are based on the principle of counting and irrationals are not countable. I'm waiting.