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Another proof simple now THAT NO TWO LINE SEGMENTS CAN HAVE EQUAL CARDINALITY- 1. Let us start with the assumption that any two line segments have equal cardinality. 2. Take any 2 line segments say line AB and line CD of arbitrary lengths. 3. Consider arbitrary point P on line CD. 4.Now segments AB and CP must have Cardinality equal (if any 2 line segments must have equal cardinality). But now the points of portion PD are left over, ie extra. Hence line segments AB and CD can not have equal cardinality. 5. Since AB and CD are any two arbitrary line segments, hence now:- no two line segments can be of equal cardinality. (Aug 25, 2013 | post #9577)

A watch placed higher will be running faster? How does that happenYes to locate a point in spacetime would require (x,y,z,t). I know that. In that sense, time is a dimension. But will keep trying to think 'out of the boxLike a curved 2D plane? Hmmm, boggles the mind. What if time flows UNevenly? (Aug 25, 2013 | post #9576)

Well Cantor had to say stuff that was counter-intuitive. But I am not giving up so soon :) Cause even though the mapping may be one to one, the points on the 2 meter line segment now have to be longer than the points on the 1 meter line. If all points are identical, then some points on the longer line must thus be skipped as you draw lines of correspondence. OK you may say instead of drawing infinite no. of lines to do the mapping, we continuously sweep the line that establishes one to one correspondence, then there is clear one to one points in each line this way. CRAP. -But the size of the points must be different on both lines this way, as is apparent from the geometry. Now the points on 2 meter line must be larger than points on shorter 1m line; so now points on 2m line are now of non-zero length. Which can not be. So cantor disproved! Second approach Approach- Also can we show that their cardinality are NOT EQUAL. Illustration:- If we place the two line segments parallel again, but align left points of both to fall on a perpendicular transversal. Now we sweep the perpendicular transversal over both lines from left to right. NOW we still have one to one correspondence with all points on 1 meter line with all points all points on 2 meter line upto the mid point! Since there are points still left over on 2 meter line, thus the cardinality are shown to be NOT EQUAL Infact cardinality of 2m line is more. (or we can just sweep the line used to establish one to one mapping from a point OTHER than the point of intersection of the two transversals joining the ends of the two || lines. If we sweep this line for the mapping, after it has covered all points of one line (reached its other end), points will always be left on the other line, hence cardinality shown not equalWhat I was merely saying was, we can not just integrate an nth dimension space to 'create' another dimension. The results will remain in a mathematician's mind only. Integrating wont create a dimension, but if a dimension already exists, then the integration can be used to describe it. Describing stuff that don't exist, is fiction no matter how interesting. [Forget the 4th spatial dimension, Can you show any of the 'known' dimensions are for real, and not just "IN OUR MINDS"!] 2D spherical surface is interesting. We sort of live on one. (Aug 25, 2013 | post #9575)

I used to think so too. Wrote a poem about that in 2007. Sort of still do. But then again, is that only for beings like us? (Aug 24, 2013 | post #9564)

That I can agree with. It gives us the sense that we only exist in the present. Fact is, we perceive our existence using our senses. And as we get our sensory information, whether external or internal, we perceive as the PRESENT INSTANT. We are such beings that we can get input information only one pattern at a time, so we can see only only point of time. [Then I could be wrong, but at least I trying to see things differently.] (Aug 24, 2013 | post #9563)

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