12-31-2005, 09:01 AM
Pete,Dec 31 2005, 12:42 AM Wrote:Hi,
Yes. Consider the set of positive and negative integers: {. . ., -2, -1, 0, 1, 2, 3, . . .}. Without getting into advanced set theory, this set is countably infinite and yet (assuming the axiom of choice) it has no 'first' or 'last' element. A simpler example, {all flatware in your house} is a finite set that has, a priory, no ordering principle -- any element of that set could be designated 'first', or if you prefer, no element can be.
As to cause and effect and effects needing a cause, that simply leads to an infinite regression. One must either accept that, postulate a 'first cause', or give up some part of casualty. All three are perfectly acceptable philosophical grounds. But that is not the only viable viewpoint. There are many other possibilities: our 'universe' may be a bubble in something that is infinite in time; the curvature of our universe might have been sufficiently great prior to the initial expansion that time was curved onto itself so that it was infinite but bounded; our universe might still be a gravitationally bound object that expands, contracts, rebounds and goes on like that forever in both the past and future. Frankly, we haven't been doing science long enough to have more than a notion or two.
--Pete
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Well if you want to get into allegorical mathematics, 1 is really the origin of all countable numbers in additive space, as all other numbers are recursively derived from it. Given that the space is arbitrarily large, though, any number that normalizes itself can become the origin. Kinda buddhist, really.
Great truths are worth repeating:
"It is better to live in the corner of a roof
Than in a house shared with a contentious woman." -Proverbs 21:9
"It is better to live in the corner of a roof
Than in a house shared with a contentious woman." -Proverbs 25:24
"It is better to live in the corner of a roof
Than in a house shared with a contentious woman." -Proverbs 21:9
"It is better to live in the corner of a roof
Than in a house shared with a contentious woman." -Proverbs 25:24