Quote:
Originally Posted by Barrykgerdes
Sorry Carl and Steven
You have both decided to give infinity a meaning that it hasn't got.
A standard human mind trait that must try to explain something that can't be explained. To say that infinity is smaller than smallest or larger than largest is still giving it a meaning that is not infinity. Once the mind can understand infinity most of the other bounding consepts we have will start to have a new meaning.
Barry
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You still don't get it
Take a time period of 1 second....how many time intervals can we divide that 1 second up into??. Take a time period of 1 billion years....how many can we fit into an infinite period of time??
Infinity is both small and large. Small and large are bounds of scalar convention, not bounds of length, volume, area, time etc etc. Something can be infinitely large or small. Anything can be divided up into an indeterminate number or quantity of whatever you chose it to be divided up in.
It's what Steven is trying to get at.....say you have a set N, that has 10 integers (the numbers 1-10) in that set. Common sense would tell you that it is finite in size and there is only 10 numbers there. But you would be wrong.....what you have there is an infinite set of numbers. The cardinality equals 10 (because there are 10 integers within the set). However, for every integer (1-10) there is an infinite number of elements, n, that each integer can be divided up into and that have values between 1 and 10). You have defined set points for the beginning and the end of the integer sequence, however you have an infinite number of possible values present between those end points.