“Actual infinity” How it works?

Scholar Asked on May 30, 2017 in MATHEMETICS.
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Any thing (object or parameter) which has no effect (or some time negligible effect) of its presence on other object or parameter, in a sense one feel absence of other, is an actual infinity.

Example.

  1. A well known phenomena: positive charge has an attractive force on negative charge ( or repulsive force on positive charge). If you fix one and start making slowly other away from one, the force starts getting reduced. At certain distance, there is no force experienced of one, by the other. This distance (and more than this distance) can be considered infinite distance in this case.
  2. One can eat multiple banana but there is a limit beyond which it is not possible to eat. Those number (in this case) can be considered as infinite
Scholar Answered on June 1, 2017.
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Infinity is a difficult and subtle concept; Aristotle distinguished between actual and potential infinity.

The potential infinity is like the sequence 1,2,3,…

You know you can always go on, but at any point of time you have only a finite set of numbers; and not an infinite one; so Aristotle could justifiably say this was only infinite potentially, as you by your hand haven’t grasped an infinite set of numbers.

Aristotle considered that sensible (ie physical in contemporary scientific language) can only ever be potentially infinite; and never actual; and this has generally been the case: consider that singularities (infinite density) in black holes are problematic, as are infinities in Feynman Diagram calculations in QED, or infinite speed.

So, what about actual infinites – are there any such things?

Well, mathematics can complete the sequence above; this new ideal element is called omega; but the same problem that Aristotle identified creeps up again – but more subtly.

Since we can have omega, omega+1, omega+2…

However, at any point of this sequence we, unlike the earlier example, have an infinite set; so strictly speaking Aristotle was wrong here; but in a larger sense he was right since this infinity is still incomplete.

Scholar Answered on June 4, 2017.
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