Re: Galileo's Paradox
Eckard Blumschein wrote:
On 12/5/2006 7:20 PM, Tony Orlow wrote:
When we divide the line by this number, we get one point,
This is the trick which provides anything. Are you reaaly so naive?
The pot calling the kettle black. People who live in glass houses
shouldn't throw stones.
the 0D square.
There's really no way you can convince me that the cube does not have
infinitely more points than the square, or the square than the segment,
or the segment than the point.
Even Georg Cantor eventually accepted this while being hampered by the
same kind of intuitive thinking like you. He wrote: Je le vois, mais je
ne le crois pas.
These are different levels of infinity.
You did not even understand Cantor. How will you understand me?
Actually, that's a good question.
--
David Marcus
.
Relevant Pages
- Re: Galileos Paradox
... What would larger than infinity mean? ... What,in mathematics, has a solution which is neither a real measure, or the measure of truth of a statement, 0, 1, or somewhere in between? ... We have the unit square, consisting of an equally infinite number of distinct parallel unit line segments. ... There's really no way you can convince me that the cube does not have infinitely more points than the square, or the square than the segment, or the segment than the point. ...
(sci.math) - Re: Galileos Paradox
... What would larger than infinity mean? ... When we divide the line by this number, we get one point, the 0D square. ... or the segment than the point. ... quantitative elements are mapped by formulas referencing their values. ...
(sci.math) - Re: Galileos Paradox
... What would larger than infinity mean? ... We have the unit square, consisting of an equally infinite number of distinct parallel unit line segments. ... There's really no way you can convince me that the cube does not have infinitely more points than the square, or the square than the segment, or the segment than the point. ... As far as sequences go, we can also distinguish between different infinities, certainly where one is a subset of the other, but also where quantitative elements are mapped by formulas referencing their values. ...
(sci.math) - Re: Galileos Paradox
... What would larger than infinity mean? ... the purpose to quantify is an important aspect of mathematics. ... infinitely more points than the square, or the square than the segment, ... or the segment than the point. ...
(sci.math) - Re: mr Normans perpetual flying machine.
... They don't matter. ... For an example the classic summability of te geometric series ... equals 1/3 of the unit square. ... You need to have the notion of infinity. ...
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