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+--- Thread: Are there "higher" and "lower" infinities? (/showthread.php?tid=3449)
Are there "higher" and "lower" infinities? - Dark Jaguar - 11th January 2006
Well, let's see!
First test, there are infinite whole numbers. Are there as many even whole numbers (2,4,6,8) as there are both even and odd whole numbers?
Both are infinite, so you'd have to conclude "yes". After all, name any whole number you can think of and I can give you an even number to match it "set for set". I'll just double your number!
You: 1
Me: 2
U 4!
M 8!
U 8
M 16
U 10000000
M 20000000
U -5
M -10
U Infinity
M Infinityx2
I'll match every unique natural number you come up with with an even number, EVERY one! It won't stop!
But, that just doesn't SEEM right does it? By all rights, the number of even numbers should be "half of infinite" or something, shouldn't it? Or, are there greater and lesser infinite sets? Seems more likely, but how defined? How about definining them by their limitations? Yes, infinite sets can have limits. The infinite set of even numbers is limited to even numbers for example. Odd numbers are absent, and yet it is still infinite.
Next riddle: is .9999~ < 1?
Same issue, that number gets closer and closer to 1 forever. Any single number you can ever list, that number will beat it. There is no "in between" number you can ever name. The only time this stops is when you name "1", so that's it's limit.
So... .999~ = 1
So then, why did I bring this up? Well, for those of you that already knew this, and I know anyone who's taken a decent math class does, never mind this. This is for a couple people who in the past didn't seem to get that infinity can have limits.
Are there "higher" and "lower" infinities? - EdenMaster - 11th January 2006
...
Are there "higher" and "lower" infinities? - lazyfatbum - 11th January 2006
You're taking certain liberties with assumptions and using intuition in place of logic, so in that sense yes it's true. You could also assume that 0 is nothing and you cannot have less, or 'more than' less, you could also assume that any given number is a set limit and no longer infinite.
But for what it is as a constant logically, it is a completely infinite system. Though it should be stated that other than in math itself, there is no such thing as to be counted infinitely as everything univesally applies itself to cycles to which it begins at any set point and ends at any set point yet continues as a cycle, such as a watch. The term 'infinite' is then applied for the fact that the cycle never ends except for billions of variables which alter the cycle over time to which it could hypothetically reach a point within its cycle where it can no longer function (destroyed, absorbed, etc).
But yeah, numbers themselves are wholly infinite but completely useless, they act only as anchors to the abstract or for scientific purposes in experimentation. You could say the mammalian brain has around 1,000,000,000,000 neurons, or you could say the mammalian brain has around 'apple' of neurons, as long as you apply the value of the number to a name or system it becomes meaningless to only focus on one system though it's used for universal appeal, which I understand.