Read e-book online Approaching Infinity PDF

By Michael Huemer (auth.)

ISBN-10: 113756086X

ISBN-13: 9781137560865

ISBN-10: 1137560878

ISBN-13: 9781137560872

Approaching Infinity addresses seventeen paradoxes of the countless, such a lot of that have no regularly authorized strategies. The booklet addresses those paradoxes utilizing a brand new thought of infinity, which involves that an enormous sequence is uncompletable while it calls for anything to own an unlimited extensive magnitude.

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Extra resources for Approaching Infinity

Example text

Typically, when a thing is made up of parts, we think that the thing depends for its existence on the existence of those parts, and that the thing exists at least partly in virtue of those parts existing. So the one-meter line depends for its existence upon, and exists at least partly in virtue of, the existence of the left half and the right half. Similarly, the left half depends upon the left quarter and the second quarter; the leftmost quarter depends upon the leftmost eighth and the second eighth; and so on.

First, it does not seem that the game is worth anything close to an infinite amount of money. Indeed, few people would value it even as high as $20. Is our intuitive valuation mistaken, or is there something wrong with the reasoning of the preceding paragraph? 19 This problem was originally published by the Swiss mathematician Daniel Bernoulli in 1738, who attributes it to his cousin Nicolas Bernoulli, also a mathematician (not to be confused with Daniel’s brother Nicolas Bernoulli, who was also a mathematician).

10 Zeno had a third paradox, but it is too lame to include in the main text. It seems to involve inferring, from the premise that an arrow in flight cannot move any nonzero distance at a single instant of time, that the arrow is at rest at each instant, and thence that the arrow never moves. 26 Approaching Infinity Some students who hear of this puzzle draw the conclusion that the ball will get closer and closer to the ground but never quite reach it. This is wrong. If the above reasoning is correct, then it can be applied to any object and any chosen destination point.

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Approaching Infinity by Michael Huemer (auth.)

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