David Cameron
Nov 2005
Junior Member
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quote:
Originally posted by doctor zoidy
my calc teacher always defined infinity as "to grow without bounds" which makes it more of a verb than a noun really, but the concept is sound, that it is not actually a number, but an irrational concept. you rarely see it in everyday math, unless your calculations of f(y) as x approaches infinity... but then again, you rarely see midgets around here, and i'm sure there are plenty in hiding.
Infinity is a perplexing concept -perhaps beyond the reach of human imagination. No wonder confusion abounds regarding its essential nature! The resolution of its true identity lies in the definition of number, which proves as elusive as infinity itself. In the midst of this confusion, mathematicians, philosophers, science-fiction writers, and the general population remain adamant in their claim infinity is not a number. Yet what supports this claim, if not a good understanding of number? Is the claim simply a stagnant belief, destined to die out slowly, just as when zero was once thought not to be a number? This appears to be the case, in light of tremendous support for the claim that infinity is a number, and a poignant shortage of evidence to support the opposite.
Five arguments claiming infinity is not a number have been presented, each one shown to be lacking. Infinity cannot be written in standard notation, but only because our number system is designed for writing finite numbers. Infinity may not be identifiable in the world, but neither are many other numbers that we deal with. Infinity does not simply mean endless growth this is only how it is used when performing limits, not when it is used to describe the cardinality of a set. Infinity differs from finite numbers in the properties it exhibits, but using properties to define numbers is superfluous and begs the question. Mathematicians working with formal systems can choose to work with whichever entities they so choose, but this does not affect the underlying logical reality numbers still exist regardless of what formal system is employed.
In order to clarify the issue, three clear and unambiguous definitions for number have been proposed: infinity as the sort of thing we can tally; infinity as an indicator of quantity; and infinity as an abstract logical object that is equinumerous to some conceivable set. None of these conceptions of number conflict, and each one of them supports the idea of infinity as a number. These three definitions stand unopposed, as competing theories have been shown to be faulty. The acceptance of only one of these three definitions is sufficient to conclude that infinity is a number.
There is nothing left that remains to be said; the opposition has failed to provide a supporting framework for their claim, whereas several viable definitions of number that include infinity have been proposed. Advancement in the understanding of infinity will not come as a result of research illuminating the issue; it will come as a result of intellectual communities accepting what has already been demonstrated: infinity is a number.
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10-06-2007 05:36 PM
