@vondesastre

When will we see prototypes small scale?

regards

I think that there has to be an infinity because dividing any number by zero yields an infinite value.

x/y=z

As y approaches zero, z approaches infinity

That is interesting. However, if let us examine the truth of the statement by demonstrative logical example:

If true then 5/0 = infinity
If true then 3/0 = infinity
If true then 5 = 0 * infinity
If true then 3 = 0 * infinity

Therefore we start to see a problem, as both statements cannot be true. Which is the truth then 0 * infinity = 5, or 0 * infinity = 3?

Or are you stating that it is an equivalency thing..... which would yield 5 = 3, since 0 * infinity is equivalent to 0 * infinity ........

ALL division problems are falsifiable through built in mathematical functions.

For instance, multiplication can be falsified with addition

3 * 2 = 5 (falsifiable statement)
2 + 2 + 2 = 6 (equivalent function demonstrating first statement false. In this case addition.)

You notice that 2 added to 2 a total of 3 times, is to state the multiplication of 2 * 3. It is a different means of stating the SAME thing, but in long hand. It is solved by linear computation.

2 + 2 = 4
4 + 2 = 6

Let us examine this relationship to 5 = 0 * infinity

0 + 0 = 0
0 + 0 = 0
0 + 0 = 0
(do I need to go on? Even an infinite number of additions of 0 to 0 will ever reach anything but 0 .....)

Now, what is 0 * 5? Why it is 0!
What is 0 * 3? Again, it is 0!
What is -5 * 0? Yes 0!
what is .5 * 0? AGAIN 0!

NOW WHAT IS 0 * infinity? ....... 0 .......

Therefore, 5 = 0 * infinity states that 5 = 0 ..... Is that a balanced equation??

What it demonstrates is that infinity cannot correspond to any real number, since all built in mathematical falsification techniques merely do not matter to the adherents of the concept. The concept is prettier than the truth.

Truly, I challenge anyone to mathematically PROVE the mathematical concept of infinity mathematically, as I will state again "extraordinary claims require extraordinary proof".......... (All other truthfull mathematical concepts can do such.)

I can prove why x/y=z, can you? It will be an interesting debate at the very least for all!

Paul Andrulis

pi, prime numbers, parallel postulate, and the best for last:
Take any positive or negitive number and divide it by 2, forever...
It'll never stop dividing. No matter how many times your try...

Untill you find an end to these "infinite" phenomenon its all theory.

You don't have to understand infinity to see its function.
~Dingus Mungus

Good points! Some of this I have dealt with already previously in this thread, but I will reiterate. Some of these are new arguments.

First, concerning PI, there is absolutely no proof that it is infinite. None whatsoever. We have not found the end of the progression, but that does not mean that at the ten thousandth or even millionth decimal point it does not end. If it ends, it it not by definition infinite. You see the problem?

Second, concerning parallel postulate, is it possible to have a warp in space time which will bring these two lines infinitely close, which is the definition of intersection? 

Lastly, the divide by 2 and prime number problems, of which the answer is the same. I stated to the effect previously that "infinity" is a derivation of the imagination, and only has relevance according to pure mathematics. For instance, you did not mention another of the same type, namely what is the largest number possible, of which the answer is non-sequiter, since you can envision the largest number you can envision, then just add 1.

Infinity is purely an abstract concept, with no reflection in reality by which we can judge the truth of the statement. Abstract concepts are the only statements made by the mouth of man which tend to be non-falsifiable. My challenge was made tounge in cheek, since even with "prime numbers" and the "divide by 2 rule", it would require more than your life span to prove the concept mathematically true, WHICH NO ONE HAS EVER DONE!  There is a point which you have to truthfully state you ASSUME but you do now KNOW.

Also, by definition  infinity is both the largest number possible, and has no end. These are actually two definitions which are incompatible, as EITHER it is the largest number possible (of which cannot be increased by any means), OR it has no end.

Yet, I can legitimately state mathematically x = 5 * infinity which increases the number falsifying the first definition.

I can also with equal mathematical legitimacy by currently accepted rules state x/0 = infinity, or x = 0 * infinity, which yields the only possible number for x in a self limited equation as x = 0, which means infinity is either 0 or 1 (0/0=0 practicle or 0/0=1 purely mathematical under x/x=1), which effectively puts a definitive limit to infinity, thereby falsifying the second definition.

Neither definition can be therefore true. Something is clearly wrong, since infinity is used as both variable and constant at the same time, and cannot fulfill the basic rules of valid mathematical functions in that any equation using infinity is by definition either unbalanced or self negating.
 
It exists my friend, only in our minds for those numbers which are too grand for us to comprehend, in a rather poorly formulated manner.

ALL THEORIES are falsifiable, and infinity itself is still but a theory.  The rules of falsification apply.

To mathematically prove anything, you have to use math, not other equally abstract and unfalsifiable concepts such as infinite progression such as primes, infinite division by 2, or infinite anything. These are all self referencing, when trying to prove infinity.

That is why this will never be proven MATHEMATICALLY, though it's mathematical useage is easily disproven mathematically  , because the only means to prove infinity is abstract self-reference, which has never been stated as acceptedly valid as a means of proof for ANY theory.

To put this in perspective, I cannot prove the validity of a private theory by saying "because my theory says so". I have to demonstrate mathematical or observeable extraneous proof, and preferrably both in quantity, for the purpose of allowing others to mathematically and logically examine and determine its applicability to reality. (the principle of falsification)

I shall broaden the scope, and loosen the inherent restrictions, of the challenge. Prove infinity, by utilizing EITHER mathematics or observeable reality, with the clarification that your proof must not be self referencing in the manner described above.

I have read many posts here, and I think most are up to the challenge, though I truly do not think any will accomplish this. (Not because of intelligence, which many demonstrate in quantity from my observations, but due to my perceived inherent impossibility of the task.

PLEASE NOTE that I am not attacking nor insulting anyone. I am attempting to give you a concept upon which you may challenge both myself and yourselves as well, with some healthy mental debate.

TO WHAT PURPOSE? If infinity is truly not applicable to reality, then the various concepts based upon its inclusion (such as say the speed of light acceleration "barrier", etc...) are self falsified. It will improve science as a whole.

Paul Andrulis

The radii. simply draw a circle observe the circle is 2D. it has an inner radius and an outer radius. this is where the parallel postulate comes in. it is observed that the inner and outer radius will never intersect. they will always be parallel to each other. In a 3D form the radii is a ring it carries the same properties an inner radius and an outer radius. In addition the ring representing the radii and being a 3D form carries inherent properties. it has a top and bottom which is also parallel to each other and as the inner and outer radius the top and bottom will never intersect. in addition to these properties Pi is present on the surface of the entire form.

How this fits into infinity. The parallel path that never intersects is indeed infinity. If something, anything could travel a path indefinitely with no observable deviations in that path than it is indeed infinite. Unity is in part or whole the radius of the natural sine. if this is true than a ring is unity by form alone. over unity would be to simply spin the ring in an annular motion about it's pseudo axis. 

"Untill you can show me the end of a infinite mathematical function I'm forced to still believe they continue on forever.

~Dingus Mungus

P.S. What evidence do you have that pi or prime numbers will eventually end?"

Dingus, your PS is the best question you have asked me. I hope my answer is satisfactory.

Mathematics is a tool. Pure and simple. It has to reflect reality in its useage to be of any defineable value. That is mathematics purpose for existance. However, any tool can be abused or manipulated. Mathematics in this manner can be related to a painters brush. A painters brush can be used to paint a truly awesome depiction of the wielder's view of reality, or it can be used equally absractly to portray something that either does not or cannot exist in nature, or is a horribly blurred and unuseable rendition.

Occasionally, as with the artist Escher, you end up with art that imitates reality quite closely, but has aspects within the picture which are impossible, while the rest of the picture in question dutifully reflects reality. These types of picture are, at first glance, quite realistic, until scrutinized closely. Mathematical paintings of reality are generally of this type. Unlike a mere painting though which can at best give a semblance of reality, mathematics paints a picture which we accept as the understood reality of our universe. It is the main tool which we use to describe reality. Therefore, in all aspects mathematics should in every case reflect reality, and reality mathematics.

Now I define reality as: The natural universe and everything existing in it both visible and invisible, past, present, and future, whether apparently material, energy, or force, or any aspect or combination thereof.

The problem with infinity in its relation to reality is that NOT ONE THING in reality has been demonstrated to be infinite. Not one. At any given point in time, everything from the amount of universal mass, the size of the universe itself, the numbers of any given particle, etc., etc., etc., are all finite. The universe is expanding, which it cannot do if infinite. The amount of matter, and therefore mass, of the universe has been shown to be decreasing, which cannot be true if the numbers of particles etc. were infinite, in which case the amount of universal matter and mass would be infinite.

Therefore, if you have a reality which is demonstrably finite, the tool which portrays said reality is therefore finite, as well as all useages of it which demonstrate reality. Therefore, to answer your question, all functions of mathematics are limited to reality, or are therefore nothing more usefull than absrtact art. Something which may appeal to the senses, but demonstrates no clear aspect of reality, and is unuseable in its representation thereof.

Prime numbers are limited to the largest APPLICABLE prime, if they reflect reality.

The largest number in mathematics is the largest APPLICABLE number.

Concerning either of the previous two, any number, prime or other, no longer reflects reality, but is in fact abstract in nature.

Concerning PI, all other real ratios deplete eventually, therefore I have more evidence that it eventually ends than I have that it doesn't, therefore can statistically state that it probably does end, even if I have not found where.

Nothing in nature is infinitely reducible, therefore nothing in mathematics is either.

No path in nature is infinite, as all have starting and ending points, even if these paths are from universal boundary to boundary. Not even the path of a circle is infinite, since said path IS THE CIRCUMFERENCE, and no circle is of infinite circumference, not even a circle encompassing the boundary of the universe itself.

That is why infinity is unfalsifiable. It has to be self referencing, since nothing reflects it, and it is nowhere referenced by anything real. It is, as I stated before, an abstraction of mathematics, and therefore useless as a concept in science, as science is by definition the study of the natural universe (reality).

I shall quote Wattsup, as he demonstrate the illogicality of the self referencing concept quite succinctly, and is right in that it is a mental trap.


"If 0 equaled infinity and having total zero of something is impossible - then no infinity is correct. If 0 does not equal infinity, then all the numbers in the world, on either side of zero could not match infinity either. So the only logical answer left is 0 = infinity, but if total zero of something is impossible - then no infinity is correct again.

Infinity = never ending worries about infinity
No infinity = Closing the book on this subject
It's a no win question or trap."

Paul Andrulis

I would have to disagree with your assumption of the finite universe. A little knowledge of quantum mechanics and virtual particle theory would tell you that the things holding reality together are infinite as far as science can determine. Virtual particles pop in and out of existence on demand to perform most of what consider work or energy. This is mostly theory, but we must look at our past and see that we're never 100% right, just on the right track. Most of our fact is estimation, as in not exact and only applies to that which we have physically confirmed.

To not believe in infinity is quite paradoxical when considering existence at all. It's much like the chicken and the egg. If the big bang came from _____, then how long was ____ there? What came before _____? When everything in the "finite" universe slows down and gets cold due to entropy, then what happens to it? How long will it all just sit there? Will it ever go away? Doesn't it require a lot of energy to destroy or remove all of reality? How do you destroy the left over energy when all mass is converted to energy? How long will that energy exist for? Finite thinking is understandable but not scientific... Infinity is a concept that can't be properly explained with words or numbers. You see the function of infinity all around you everyday, I know you do, but we will never physically see it or understand it.

An interesting debate, but much like a god, infinity can not really be proved one way or the other at this point in the human existence.

~Dingus Mungus

The reason why

5/0=0
3/0=0
0=5
3=0
5=3

appears to be false or contradictory is because of the frame of reference you are applying to the value zero

Hans states correctly  "If we think of zero as what it really is, namely nothing,"

however this statement does not impart the full meaning of zero.

Math deals with all subjects in an absolute sense. The absolute value of zero is actually the absence of anything, the absence of everything.
It is the exact opposite of all that is. If you can imagine the distance between nothing and everything then you have clearly failed to space them far enough apart. The inverse is also true, you have failed to recognize that there can be no space between something that does not exist and something that does.

When examined from this perspective, the value of 0 is infinitely less than the value of 1 or any qauntity. It is not simply 1 unit less because that would leave something to be examined. 0 nullifies the existence of any number.

Carried further 0 is also infinitely greater than everything that is. "Nothing" is the proverbial +1 ad infinitum. If nothing is discovered it becomes part of everything, proving that it was something.  

In this same sense the value of 1 and of any number is infinitely greater than the value of 0.

Math amazingly recongnizes this relationship. And when asked a question about everythings relationship to nothing it gives the following reply:

 IF 5/0= 0
 IF 3/0= 0
 THEN   5=3 , 5=0

By interacting "everything" with "nothing" math shows clearly the relationship between the 2.

5 is = to 3  from 0's perspective because both numbers are equally greater/lesser than the existence of nothing.

5 is = to 0 from maths perspective because they are equally probable.

Mathematics does not acknowledge its own existence as definitive proof that it does not exist. It should however be noted that it gives "nothing" very few comments seeing as how it only mentions 0 once but talks about everything forever. 12344567891011121314151617181920212223242526272829......

For anyone that doubts my analysis please review the following proof of infinity:

IF 5/0 = 0
IF 3/0 = 0
THEN 5=0 , 3=0 , 5=3

"Proper use of Mathematics doesn't lie. Its just the way people interpret the answers math provides that mucks things up."
Sky

Quote from: Super God on August 21, 2007, 04:34:10 AM

I think that there has to be an infinity because dividing any number by zero yields an infinite value.

x/y=z

As y approaches zero, z approaches infinity

That is interesting. However, if let us examine the truth of the statement by demonstrative logical example:

If true then 5/0 = infinity
If true then 3/0 = infinity
If true then 5 = 0 * infinity
If true then 3 = 0 * infinity

Therefore we start to see a problem, as both statements cannot be true. Which is the truth then 0 * infinity = 5, or 0 * infinity = 3?

Or are you stating that it is an equivalency thing..... which would yield 5 = 3, since 0 * infinity is equivalent to 0 * infinity ........

ALL division problems are falsifiable through built in mathematical functions.

For instance, multiplication can be falsified with addition

3 * 2 = 5 (falsifiable statement)
2 + 2 + 2 = 6 (equivalent function demonstrating first statement false. In this case addition.)

You notice that 2 added to 2 a total of 3 times, is to state the multiplication of 2 * 3. It is a different means of stating the SAME thing, but in long hand. It is solved by linear computation.

2 + 2 = 4
4 + 2 = 6

Let us examine this relationship to 5 = 0 * infinity

0 + 0 = 0
0 + 0 = 0
0 + 0 = 0
(do I need to go on? Even an infinite number of additions of 0 to 0 will ever reach anything but 0 .....)

Now, what is 0 * 5? Why it is 0!
What is 0 * 3? Again, it is 0!
What is -5 * 0? Yes 0!
what is .5 * 0? AGAIN 0!

NOW WHAT IS 0 * infinity? ....... 0 .......

Therefore, 5 = 0 * infinity states that 5 = 0 ..... Is that a balanced equation??

What it demonstrates is that infinity cannot correspond to any real number, since all built in mathematical falsification techniques merely do not matter to the adherents of the concept. The concept is prettier than the truth.

Truly, I challenge anyone to mathematically PROVE the mathematical concept of infinity mathematically, as I will state again "extraordinary claims require extraordinary proof".......... (All other truthfull mathematical concepts can do such.)

I can prove why x/y=z, can you? It will be an interesting debate at the very least for all!

Paul Andrulis

Hello all!
I am really only trying to help here, so please do not take this as me being a jerk.

I’m a mathematics major in school(just a few more classes, woohoo!) and I can tell you there is nothing wrong with our number system. Did you know there is more than one infinity and that some are larger than others? Sure, we use different symbols for different infinities that aren’t 0123456789. There are an infinite number of infinities between 0 and 1. Trust me, finite minds can understand infinities. Sure, it’s a horrible mindf**k at first, but we eventually do. If you want to understand infinities, study the work of Georg Cantor. Study some Real Analysis, Set Theory and Number Theory too. If you can understand a basic derivative in Calculus 1, you understand infinity using our number system.

As for Pi, it is not an integer. It is an irrational real number. Its decimal representation is infinite. It is a simple ratio of a circle’s circumference to its diameter.

Don’t get too philosophical with this stuff guys. It really isn’t anything to philosophize about.