StarCraft® II

To infinity, and beyond!

Posts: 149
Since so many threads eventually end up here anyway, why don't we settle this once and for all.

Infinity-1 < infinity? -infinity = 0?

Are 0 and infinity mathematical truths, or abstract ideas, constructions of the human mind?

I would argue that they are simply constructs. By definition, there is nowhere in the universe where there is nothing. The simple act of observing nothing would make it something, so nothing is not something we could have learned from nature. 0 is a concept humans have created.

The same argument can be applied to infinity. Observing an infinity is, by definition, impossible. The big bang indicates that the universe is, in fact, not infinite in length, and a finite universe could not contain any infinities. If there is nowhere in the universe that we could observe an infinity, it must have be something that humans have created.

These two concepts are useful, but they are very different from the rest of mathematics. Because they are simply ideas, it is entirely possible for them to diverge from nature- an imaginary infinite is far less problematic than a true infinite, and while we can never observe nothing, we can certainly think it.
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03/20/2012 02:41 PMPosted by capnpufnstuf
I would argue that they are simply constructs. By definition, there is nowhere in the universe where there is nothing. The simple act of observing nothing would make it something, so nothing is not something we could have learned from nature. 0 is a concept humans have created.


i kinda view it as if i have 5 applers and someone takes 5 apples from me then i have zero apples...but yea if you expand it to the universal scale i would say that no where is there nothing at all...even though i believe that the universe came from nothing through intelligent design that is off topic jsut wat i believe
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yea thats how i see it astrai...if you get specific enough like no leprechauns on earth then yea you can get zero but you cannot know that there is no leprechauns somewhere however unlikely it may be...
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Infinity, however, is a concept and not a number. It has no specific value associated with it



This.
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No I can safely say there are no leprechauns in the universe.


Not... exactly.

The best we can say is that it is as most likely untrue as something can likely be untrue.

We cannot however suppose to have a process of making determinations of negative proofs because we do not have a means of verifying this across all of reality.
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03/20/2012 03:11 PMPosted by Astrai
You can do operations with it, and in fact mathematics as we know it would not exist without zero.


Math as we know it. People can (and did) perform mathematical calculations without 0, but good luck trying to do math without any 1's or 9's. There's simply no way it could work.

03/20/2012 04:07 PMPosted by Astrai
Now, new evidence can come to light which would change that conclusion - but until evidence comes to light, disbelief is the only rational position!


There is an important difference between knowing and believing. Besides, leprechauns are imaginary, so of course you can measure them with an imaginary number ;)
Edited by capnpufnstuf on 3/20/2012 4:29 PM PDT
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The standard is not 'existence until proven to not exist.'

The standard is 'does not exist until proven to exist.'
What about probability? A lot of people who claim to be rational thinkers publish theory as fact and vice versa all the time!

03/20/2012 04:28 PMPosted by capnpufnstuf
People can (and did) perform mathematical calculations without 0, but good luck trying to do math without any 1's or 9's. There's simply no way it could work.

The ten digits 0-9 are simply notations used for representing quantity. You could perform calculations with only the digits 1 and 0. It would just monumentally harder.

(1 + 1 + 1 + 1) * (1 + 1 + 1 + 1 + 1) = 1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1+1
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03/20/2012 04:52 PMPosted by Astrai
We cannot however suppose to have a process of making determinations of negative proofs because we do not have a means of verifying this across all of reality.


The standard is not 'existence until proven to not exist.'

The standard is 'does not exist until proven to exist.'


We can NEVER "prove something does not exist".

We can only ever point out it's improbability and incongruency with known reality.

We have no means of verifying any negative refutation of something's in existence at all points at all times across the entire universe, therefor we can not claim to an absolute certainty that something does not exist.

That is why science does not waste time with these kinds of questions. Theres no point.

Noting the incredible unlikelihood of something to the point it is essentially indistinguishable from non-existence is not the same as offering PROOF of somethings non-existence across the entire universe.

Again, we can safely treat things that are unlikely to exist as if they didn't, but that is not the same as demonstrating that they dont.
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i'm with modax on this one...
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03/20/2012 05:10 PMPosted by TiberiumDSV
The ten digits 0-9 are simply notations used for representing quantity. You could perform calculations with only the digits 1 and 0. It would just monumentally harder.


I'm talking about the concept, not the character. Can you imagine a system of mathematics where nothing existed between 8 and 10? of course not. Math is, however, possible without 0.
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03/20/2012 07:15 PMPosted by capnpufnstuf
The ten digits 0-9 are simply notations used for representing quantity. You could perform calculations with only the digits 1 and 0. It would just monumentally harder.


I'm talking about the concept, not the character. Can you imagine a system of mathematics where nothing existed between 8 and 10? of course not. Math is, however, possible without 0.


You don't need numbers to do math. You can do it with abstract algebra. But the concept of zero is important.

Back to topic, infinity is a purely abstract idea. In physics, it's commonly used to simplify the theory but every one (well... every physicist) is aware that no physical quantities can be infinite.
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Demonstrating things EXIST


Is the job of serious scientist.

Philosophers on the other hand...
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03/21/2012 08:00 PMPosted by Astrai
Sure, it's not dependent on direct empirical data, but it requires logical and fit premises and conclusions.

the thing is the truth of the premises in philosophy are occaisonally more murky and unclear, and frankly philosophy is difficult to understand when you get deep enough into it.

secondly i question the premise of this thread that many threads end up debating infinity, only that one thread did.
Edited by Necromaster on 3/21/2012 10:35 PM PDT
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Is the job of serious scientist.

Philosophers on the other hand...


I'd have to disagree there too; philosophers are required to support their conclusions as well.


Oh... oh... if only that were the case, I'm certain you are well area that not everyone seems compelled to adhere to this requirement for some odd reason ;)
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