Another argument that he stated was that, “ If Achilles (a
Greek Godlike person) can run 1000 yards a minute, he will never overtake a
turtle that runs 100 yards a minute.” Once Achilles has advanced 1000 yards, the
turtle is 100 yards ahead of him. By the time Achilles covers these 100 yards,
the turtle is still ahead of him, and so on into infinity, as the following
table shows. Position Achilles Turtle 1 0 1000 2 1000 1100 3 1100 1110 4 1110
1111 5 1111 1111.1 6 1111.1 1111.11 7 1111.11 1111.111 Another argument he gives
is the one of the arrow in flight. He said, “The tip of an arrow is in one and
only one position at each and every instance of time; in other words, at every
instance of time, it is at rest. Hence it never moves.” Zeno assumes that a
finite part of time consists of a finite series of successive instances.
Throughout an instance, he says, the tip of the arrow is at one point. Imagine a
period consisting of 1,000,000 small instances, and picture the arrow in flight
during the period.
At each of the 1 million instances, the arrow is where it is,
and at the next instance, it is somewhere else. It never moves, but somehow
accomplishes the change of position. Thus, motion is an illusory, irregular sort
of thing-a succession of stills, like a movie-not the smooth sort of transition
our senses picture. All of these examples are that Cantor attempted to disprove
by forming his own infinity theories. As of now, infinity is a tentative area in
mathematics, because certain concepts involved with it have not of yet been
proven to everyone’s satisfaction. This is one of the few areas that mathematics
and science may never be able to explain completely, because infinity can not be
measured in the classic sense.
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