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<DIV><FONT face=Calibri>Rn'TK wrote:</FONT></DIV>
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<DIV>It was to forestall just such a statement that I used the word
"separately" -- I said that the traveler does not have to touch each point on
the line "separately" -- as he would if he were to literally attempt to get to
the half way point, and before that the halfway point, and before that the
halfway point....etc....of line A..............B.</DIV>
<DIV> </DIV>
<DIV>Of course you are correct that a line must be treated as a continuum,
and not as a series of discrete points, if I am ever to get from Miami to New
York.</DIV>
<DIV> </DIV>
<DIV>CM:</DIV>
<DIV> </DIV>
<DIV>This is now probably more appropriate for a math forum rather than Avodah,
but your response indicates that you were not comprehending the finer
mathematical point. By using the word "separately" you gain nothing. "touch[ing]
each point on the line 'separately'" has nothing to do with it. I imagine
you now view each step as a discrete point reached (not passing thru all the
interim points not stepped on?). You are still in need of the continuum to
guarantee the existence of the infinitely many dense "landing points."
Whatever functional description of the movement of the body over the
continuous variables representing distance and time travelled from a to b
they will have to take on ALL intermediate values.</DIV>
<DIV> </DIV>
<DIV>Btw, there is no reason you could not get from Miami to NY in a weird world
with only discrete points, so I am not understanding your need for the continuum
to get from Miami to NY.</DIV>
<DIV> </DIV>
<DIV>Kol Tuv</DIV>
<DIV> </DIV>
<DIV>Chaim Manaster</DIV>
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