Regarding the misuse of the term infinity in the Anime/Manga Forum
Both in this forum and the sub-forum there seem to be a great misconception regarding the understanding of infinity and I'd like to clear a few things out.
The infinite, like the finite is a state applicable to all types of quantification. There's nothing in-between the quantities, there's nothing near infinite and there's nothing near finite.
A set, or quantity is infinite if and only if the quantity can be described with a number. For instance the set of natural numbers are infinite due to the fact that there is no highest natural number (see picture bellow).
(please log in to view the image)
We also know that the amount of prime numbers are infinite, due to the proof bellow.
(please log in to view the image)
But I digress.
Now two infinite sets are considered equal when you can construct a scheme where for all numbers in one set are correspondent in the other set.
Now, lets compare the set of natural numbers above to the set of integers.
(please log in to view the image)
By constructing the following scheme we can see that for every natural number there's a corresponding integer.
(please log in to view the image)
Or for those who prefer a table.
(please log in to view the image)
So if you give me a integer, say the number -2010, the corresponding number would be 4021. Nonetheless for any possible integer you could provide I could provide a corresponding natural number, hence the sets are equal.
From this we learn that and infinite set does not increase in size if you multiply it or add to it.
Next we want to examine if the set of natural numbers to rational numbers.
(please log in to view the image)
What we do is pair up the numbers in the following manner to avoid the infinities.
(please log in to view the image)
And eventually for any rational number you provide, say 1/5 I'd be able to correspond that with a natural number 14.
Last edited by Astner on Sep 18th, 2010 at 08:56 PM
We've now proved that infinity to the power of a finite number is equal to itself. Keep this in mind in cosmological anime and magna debates, infinite multiverses each consisting of an infinite amount of universes doesn't mean that the infinite multiverses are greater. Since it's essentially infinity squared.
Now you can't pair up the natural numbers (or the integers, or the rational numbers) to real numbers, which is defined as follows.
(please log in to view the image) (please log in to view the image)
(please log in to view the image)
Now we can prove that the set of real numbers (which is equal to the set of complex numbers, by the same logic for why natural numbers and rational numbers are equal) can't be paired up with the set of natural numbers. Yes, we're going to prove a negative again (see prime numbers), that's what we do in mathematical analysis.
(please log in to view the image)
What's a bit more difficult to realize is that with this we've proven that through bijection we're able to construct greater infinities and that there are no greatest infinity.
So what's actually proven, and how may it be of use?
There's no such thing as near infinite, rendering the sentences such as "near infinite power" meaningless.
Infinite multiverses such aren't necessarily greater than one infinite universe, in fact the multiverse might be smaller still.
There's no such thing as unsurpassable characters since there's always a greater infinity.
Thoughts?
Last edited by Astner on Sep 18th, 2010 at 09:02 PM
My thoughts are that most authors aren't mathematicians and it's probably more sound to take their word on it than try and prove them wrong about their own works.
Can someone summarize everything he said in those two posts in one easy to read sentence? Preemptive thankees.
__________________
"The Daemon lied with every breath. It could not help itself but to deceive and dismay, to riddle and ruin. The more we conversed, the closer I drew to one singularly ineluctable fact: I would gain no wisdom here."
First, I really appreciate this type of work. Honestly, I wish more people would try to educate themselves and try to use math to interpret reality.
This is why I like you, Astner...and this is why I defend you at times.
1. Near infinite power could have multiple interpretations. It could mean that if the person is immortal, they could exert a certain level of energy for an eternity. But, they could not exert an infinite amount of energy for an infinitesimal instant. Does that make sense? Their energy infinitely restores itself, but it is finite in storage. Example: Kid Buu.
2. This assumes that the singular universe is infinite when it is not. The multiverse is not considered infinite, either. But, for all intents and purposes it is "near infinite" as the number would be so large that it is not really a tangible number. However, strictly and pedantically speaking, there would be a finite number of multiverses and, therefore, finite in number (lulz).
3. Incorrect. Infinity + 1 = infinity. Infinity - 1 = infinity. Also, you are applying a set of mathematical rules that cannot be logically be applied. For instance, a person may have power as follows: all of the power of the multiverse/2 + 1. Not matter what anyone does, they can never surpass that person: aka, unsurpassable. The best anyone else can do is all o the power in the multiverse/2 -1.
It all ties into how you wish to define a character's power. If you define it as the power used over a given period of time then no, the character doesn't have infinite power. But if you define it by their source or resources, then yes the character would have infinite power.
Now the reason for why the latter option is meaningless is because that it would make characters that that have an extended lifespan more powerful than characters with a shorter lifespan. For instance, Roshi and Vegeta. Vegeta will eventually die of age, limiting his capabilities, whereas Roshi will live on until he's killed. So given enough time Roshi would've exerted more energy than Vegeta.
But it would be folly to work with that definition.
In reality the size of the universe is decided by the density parameter, omega accordingly.
(please log in to view the image)
According to the most recent results I've seen Omega = 1.003 +- 0.010, meaning that all three options are possible. I'm sure that there are more accurate measuring but I'm also sure that the density parameter is still undecided.
The universe and multiverse I used for my example are for all intents infinite.
Read the opening posts before criticizing them. The only postulate used was the axiom of choice--which sates that if you're able to pair up every element from one set with each and every element of another set then they contain a equal amount of elements. Furthermore, we've already established that infinity + 1 = infinity, in fact we've established all the equalities bellow.
(please log in to view the image)
As I've pointed out and proven, we can analyze infinity with algebra. In fact that are various fields of research dedicated to this. See also. If you wish to engage in an argument, read through the proof posted and try to formulate a proper response.
This argument makes no sense.
Last edited by Astner on Sep 20th, 2010 at 01:03 PM
I think the real problem is that mathematicians misuse the term Infinity, which came from Infinitas which was closer to unboundness. So pretty much all those uses are correct and the whole proof thing was pointless.
In mathematics infinity is defined as a value greater than any assignable value. Of course, just as finite values can vary in size, so can infinite values.
The reason I used the mathematical definition was because it's unambiguous unlike the philosophical definitions which are vague and vary. For instance "An infinite amount of stars lighting the night sky" is philosophically correct, but not correct mathematically.
The problem is that choosing the mathematical meaning is as wrong as picking some philosophical ambiguity, you're discussing a linguistic problems and trying to cut the linguistic part of it. You're basically making a definition that makes your argument pointless.
I disagree, the mathematical definition is, once again, unambitious and logically coherent. Whereas the philosophical is vague and confusing. As numbers are relative the philosophical definition doesn't really give any insight.
But yes, one of the main principles are that we define infinity as a value beyond assignment (i.e. the mathematical definition).
By defining infinity you're defining also the idea of it being misused -not being used as by definition-, hence the problem comes from the system as you define it, it's not inherent to the reality is meant to encompass -language-.
Yes, terminology can be misused. But that's rarely the case. Especially when it comes to simple story telling such as anime and manga. When Vegeta threaten to destroy the planet the intent was clear.
If someone decided to derive a rigorous formula for how much energy it would take for Vegeta to destroy a planet, that calculation wouldn't be useless due to the possibility of alternate interpretations.
When someone says "near infinite" it's obvious that they just mean "a ****ing huge amount". The fact that you don't get this simple concept despite always claiming to be so smart means you're either dense or just trolling.
But you assume there is a calculation, and thus you create the problem -of assuming there is a correct terminology for said calculation that may not have happened-.
Adjetives are qualifiers not necesarily quantifiers, in true, near infinite conveys an idea that works in a linguistic contest and hence cannot be really considered wrong.
When someone says "near infinite" he's using paradoxical terminology, which only purpose could be to confuse. In the case you're referring to it isn't that difficult to estimate the given energy. Measured in joules; it would be to the 10 to the 32th power, or for comparison; in the same range as Roshi's Kamehameha. Both more explanatory than near-infinite.
Unambiguity and clarity in a analysis is what separates a good analysis from a poor analysis. Also, I'd advice you to read the thread before commenting on it.
It works just fine when it is left ambiguous. If a character will live forever (no end) and they can exert a force for that entire time, without stopping, then it is an infinite amount of energy.
Total force in a set can be calculated as follows:
force applied per unit time * time.
if time = infinity then force equals infinity. The end.
The only rebuttal to that is "ZOMG! LIEK....HEAT DEATH!" The my reply is "see 'no end' reference."
I subscribe to the S^3 model. It's a closed loop and finite in size. I picture the universe as being like a bubble forming in a dense fluid...but the fluid doesn't adhere to the exact set of physics that our fluids do inside the universe.
As my post clearly indicates, I read the OP. You can use whatever definition of infinity that you'd like, I'll still with the an applicable definition.
There was a mathmetician, forget his name, said that if you had a hotel with an infinite number of rooms and an infinite number of guests in each room, what do you do when a couple arrives, looking for a room?
He said, quite simple, that you just move them into a room and no one has to leave because there is an infinite # of rooms. Odd, isn't it? But, that's how it's supposed to work. Infinity - 1 = infinity. Infinity + 1 = infinity.
Check this out:
infinity/2 = infinity.
The problem with the logic in the image you posted is as follows:
2^(Na) = Na
You can do lots of math on the set of infinity and it usually ends up being infinity, still.
Na+1 still equals Na. It is not >, it is =. Always.
This is where the "postulate" errors.
It does, especially using your definition of an infinite universe and your definition of infinity. WEEEEE!
Wrong. If something is left ambiguous it leaves from for subjectivity and paradoxes.
I just don't see the benefit in applying a methodology suggesting that Roshi would have infinite energy and that Vegeta has finite energy, based of their lifespans. Or more specificity it would say nothing of the characters.
You're not allowed to select a unproven model and adhere to it as fact.
That's Hilbert's hotel and there are three variants of it. The first where there's one guest checking in, the second where there's an infinite amount of guests checking in and the final where there's an infinite amount of buses each with a infinite amount of guests checking in.
The two latter are proven above in greater detail and the first one is rather basic as the assignment would be n to n + 1.
It corresponds with the equations above c + aleph = aleph. c can be 1 and -1.
Once again it's proven above in c*aleph = aleph, set c = 1/2.
I'm not going to debate someone who can't read basic mathematical proofs. If you could read and counter it you'd point out a contradiction in the proof demonstrated above.
No, not as it was formulated. I'm not going to waste my time deciphering your poorly structured sentences in hopes of understanding what it is you want to know. If you have a question or suggestion phrase it properly.
KMC Community Forums
Sep 18th, 2010 08:52 PM
