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Infinity...

Occam's Razor

Occam's Razor

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Infinity... what a mind blow! Can anyone wrap their head around this concept?

What is half of infinity? It too is infinite.

How strange that infinity can have subsets of infinity. For example, counting by one, from one, numbers continue forever... but if you count only the odd numbers, it still goes on forever. If you count only prime numbers it goes on forever. If you try to divide a whole number into fractions, those fractions go on forever.

If you drew a circle that encompasses a value of ten, then drew a circle inside that represented all the odd numbers it would be half as big. If you draw a circle that represents all numbers, then drew a circle "inside" that represented the odd numbers, it would be just as big... if in fact one could draw an infinitely large circle.

Is infinity everything? Or is it nothing?

It's said that the universe, all dimensions, energy, space and time began from something infinitely small and is expanding into something infinitely large. Yet what we consider dimensional space is limited in size by the factor of time, in 14 billion years we estimate the boundary/edge of the universe at about 96 billion light years across, but is not expanding into anything, as everything is contained in the expanding sphere of that originally infinitely small pre-big bang.

Is there a difference between infinitely small and nothing?
Is nothing the ultimate infinity?
Is nothing actually something? Or vice versa?
Are there a finite number of infinite subsets?
 

I believe that the concept of infinity is beyond the normal human brain's ability to comprehend in full.

Most people don't really understand a number larger than than what their paycheck is. I have a friend who likes to talk economics and politics, but his mental capacity really limits his ability. So he get's confused with big numbers, like he doesn't really comprehend the difference between a million dollars, and a trillion dollars. he might say something like "the federal debt is 16 million dollars", then when I say "no, I believe it's a lot more than that", he might say "well I meant it is 16 hundred thousand dollars", then way I say "you mean 16 trillion dollars" he says "yea, thats what I said". All he really knows is that it's a lot of money.
 
imagep said:
I believe that the concept of infinity is beyond the normal human brain's ability to comprehend in full.
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and yet... i keep trying. Just can't stomach unanswered questions.

Most people don't really understand a number larger than than what their paycheck is. I have a friend who likes to talk economics and politics, but his mental capacity really limits his ability. So he get's confused with big numbers, like he doesn't really comprehend the difference between a million dollars, and a trillion dollars. he might say something like "the federal debt is 16 million dollars", then when I say "no, I believe it's a lot more than that", he might say "well I meant it is 16 hundred thousand dollars", then way I say "you mean 16 trillion dollars" he says "yea, thats what I said". All he really knows is that it's a lot of money.[/QUOTE]

Is it his mental capacity, or a failure to fill that capacity with knowledge? Just curious. What drives me nuts is people who don't understand that they don't understand.

I'm really interested in whether there is a difference between infinitely large and nothing at all. It would seem an obvious answer. But is it?
 
Nothing is a lot harder for me to entertain than everything.
 
Infinitely small "approaches" 0 in mathematical terms, and therefore is indistinct from 0. See Limits.

It you want to see something interesting involving infinity, check out the Koch snowflake, which has an infinite perimeter but a finite area.
 
Republic Now! said:
Infinitely small "approaches" 0 in mathematical terms, and therefore is indistinct from 0. See Limits.

It you want to see something interesting involving infinity, check out the Koch snowflake, which has an infinite perimeter but a finite area.
Click to expand...

Ya, fractals are amazing... and my fall back position when thinking about multiverses, holographic universes and whatever the edge of our universe is..
 
Occam's Razor said:
Infinity...
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That's a human intelligence abstract creation. Nature does not depend on the mental constructs of its subjects.

Infinity is an interest rational concept that human intelligence can deal with, but it is irrelevant to Nature.

Infinity, and Humans are irrelevant to the universe.

That's rule no 1 of what I call Cosmological Reality. [CR]
 

Nature doesn't depend on anything... whatever it is, it is. regardless of form, function or whether it produces intelligent life or not.

However, since we're here to observe it, it may prove useful to attempt to understand and describe it.

I would certainly be relieved to know that there are no actual infinities in the universe, yet so far, all our understanding, all our physics, all our math, all our observations point to infinite gravities and masses. And as far as I know, it is essential to the big bang.

Do you have solid evidence to the contrary?
 
It is impossible to truly appreciate the magnificence of the concept of infinity without being stoned.
 
I think in the case of infinity it is easier to wrap your head around what it is not. What it does not include is nothing.
 
Calculus 101 uses limits to reign in infinity. You cannot divide by zero, but you can divide by a number as it approaches zero. IE: Decimal point, 100 gabazillion zeroes, one is perfectly legit for a divisor. Limits work in a similar fashion for infinitely large numbers.
 
Occam's Razor said:
However, since we're here to observe it,
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No. We're not here to observe Nature.

We are here *and* we can observe *some(

I would certainly be relieved to know that...
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A four year college degree on a science based discipline may help with your immediate questions about the term "infinite".
 
If the universe dies, contracts and re-bangs is that infinity or round 2?
 
Paralogic said:
No. We're not here to observe Nature.

We are here *and* we can observe *some(



A four year college degree on a science based discipline may help with your immediate questions about the term "infinite".
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Assumptive condescension don't really speak to knowledge or wisdom.

I'm well aware of what's "in the box", and there are thousands looking for answers in the box. It's just kinda fun sometimes to explore outside the box... and to pose thought experiments that open to laymen. Just have fun with it... fun is something you don't need a four year degree to understand...
 
Occam's Razor said:
Infinity... what a mind blow! Can anyone wrap their head around this concept?
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It's interesting to see your excitement. You should look further at set theory and cardinal numbers, because you appear to be only speaking of the first infinite cardinal.

Aleph number - Wikipedia, the free encyclopedia

In the first lesson teaching this, we usually prove that there are more irrational numbers than positive integers. So we say the irrationals are uncountable.


You can't honestly draw circles to represent these sets. Inside if your circle, which is drawn in two dimensions, you have uncountably many line segments and uncountably many points. Since the odd integers and even integers are subsets of the countable set of integers, they are countable. So if you try representing them using the innards, or even just the boundary, of a circle then you'll have pieces remaining.


I don't buy that, because infinitely small is size zero. Geometrically, it could be a limit point.

Occam's Razor said:
Is there a difference between infinitely small and nothing?
Is nothing the ultimate infinity?
Is nothing actually something? Or vice versa?
Are there a finite number of infinite subsets?
Click to expand...

Yes, consider a sequence of solid circles at the origin, starting with a radius of 1 and cutting the radius in half repeatedly. The limit of this procedure is the point at the origin, which has zero area. However, it is not "nothing".

No, there is no greatest infinity. You can see the page I linked on cardinals. Plus, there is Russel's paradox which proves there is no set containing all sets.

Well, zero is a real number.

The last question is ambiguous. There are partitions of infinite sets which are clearly composed of finitely many sets. On the other hand, the power set (set of subsets) of any infinite set is clearly infinite.
 
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