[ flickr ]
Originally posted by Tom Hughes:
[QB]The set of all squares is an infinite subset of the infinite set of all integers.
Does that make sense ?
QB]
Originally posted by Tom Hughes:
Infinity cannot be defined ?  You learn something new everyday.
Tom
[ flickr ]
The symbol for infinity is a sideways 8, which is not symmetrical in the loops. The infinity symbol is a simplified Mobius Band.
In geometry they teach that any line of any length consists of an infinite number of points. This is of course, foolish nonsense, and leads to an inconsistent, selfcollapsing, paradoxridden geometry. The Greek thinker Xeno showed with paradox that motion was 'kinema', or a discontinuous series of frozen still positions in space, similar to the illusion of motion produced by cinematic projection of a series of still pictures.
Infinity is like a virus in mathematics. If you subtract any number from infinity it is still infinity; in fact if you subtract infinity you still have infinity and if you add infinity you still have infinity. Consequently, mathematicians consider that there must be "magnitudes of infinity". For example, if the integers are infinite then the real numbers must be of a higher magnitude of infinity because between each of these infinite integers there are an infinite set of fractions. Once introducing infinity, number loses all meaning, and you can never get it out. The virus is such that if you add in infinity, when you subtract it back out the number does not return to it's original state. Infinity makes multiplication and addition to any number have identical results, eliminating the basic axioms of mathematics. Dividing by infinity does not produce zero, it is an invalid operation, just as dividing by zero (which is not only invalid but also a meaningless operation).
Magnitudes of infinity are paradoxical consequences of an invalid concept. Infinity has impossible properties. The true condition must be that every line of every length contains a finite set of points, and the number of points must be proportional to the length of the line. There can be no infinite lines. All lines must wrap around to their origin eventually, in a loop that disappears in the region of "potential infinity". Aristotle expressed the theorem of potential infinity with the phrase "For every number there exists a larger number." He could have benefited from my theorem that "Everything real in the Cosmos is finite." Numbers are concepts, and not real of themselves. I would amend his theorem with the phrase "Every larger number is still finite." Mathematics of Infinity by Thomas Gilmore
In geometry they teach that any line of any length consists of an infinite number of points. This is of course, foolish nonsense
SCJP
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Originally posted by Randall Twede:
i have no trouble seeing that any line has an infinite number of points
Originally posted by Tom Hughes:
infinity = lim(1/x) when x > 0
Originally posted by Nigel Browne:
If a line doesn't have a start point and an end point how do you draw it?
Originally posted by Tom Hughes:
you guys are mad . Isn't zero defined as the integer > 1 and < 1 ??
and surely parallel lines never meet ..?
<i>All that is gold does not glitter, not all those who wander are lost  <b>Gandalf</b></i>
<i>All that is gold does not glitter, not all those who wander are lost  <b>Gandalf</b></i>
Make visible what, without you, might perhaps never have been seen.
 Robert Bresson
Uncontrolled vocabularies
"I try my best to make *all* my posts nice, even when I feel upset"  Philippe Maquet
Rick Hightower is CTO of Mammatus which focuses on Cloud Computing, EC2, etc. Rick is invovled in Java CDI and Java EE as well. linkedin,twitter,blog
Uncontrolled vocabularies
"I try my best to make *all* my posts nice, even when I feel upset"  Philippe Maquet
you guys are mad
Ask a Meaningful Question and HowToAskQuestionsOnJavaRanch
Getting someone to think and try something out is much more useful than just telling them the answer.
When you have exhausted all possibilities, remember this: you haven't  Edison. Tiny ad:
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