PKM from Cambridge asked me to explain this. After many days thinking about it, I developed a new theory that may change the way we think about math. (7/17/2007)"> Pino's Theory About Integers and Infinite. - Jose Pino's Projects and Tidbits.

Pino's Theory About Integers and Infinite.

After I saw the book "God created the integers", I came with the idea: "Integers doesn't exists". PKM from Cambridge asked me to explain this. After many days thinking about it, I developed a new theory that may change the way we think about math. (7/17/2007)


spiral infinite Before I start, I want to clarify something: I'm not a great mathematician or a great scientist. To be honest, I'm strugling to get a good job because my poor education. I don't have a University degree, I don't even have the money to be able to get a degree, so, most of the times, I teach myself. I'm a thinkerer and self-taught person. If you believe my theory is absolutely wrong, please feel free to give me your comments and opinion.


I like math as many other sciences. I'm not a "human calculator" but most of the times I find math easy. The way I see math is slightly different than the way it is explained on books. Even my teachers, when I was at elementary school, had a hard time with me to demostrate I was wrong.


I believe INTEGERS doesn't exist. Integers were created so we, humans, can work with math on a non-exact way. What I mean is: 1, 2, 3, etc, may exist, but is impossible for humans to reach the exact point were the integer is located. Let's see the basic "whole numbers" as my teacher taught me long time ago:


whole numbers


Simple? Not really. Math is not just negative, positive and zero. Between those lines you can find FRACTIONS, so, here is the graphic representation of fractions:




As you can see, 1 is composed by two halves, or two times 1/2. 1/2 have two times 1/4. 1/4 have two times 1/8 and so on... until infinite.


So, according to some books:


infinite fractions


That means, 1 is equal to infinite? or 1 is composed by infinite fractions? So, if ONE is equal infinite fractions, you will NEVER be able to reach one. The exact point where you believe is ONE, is not exactly ONE, in reality 1 can be 1.0000000000000000000000000000000154346538 or may be 0.999999999999999999999994534523


That is the reason why I believe INTEGERS DOESN'T EXIST. I do believe 1, 2, 3 and so on, are UNITS.


But there is a problem:. If INTEGERS doesn't exist, math doesn't exist. You can't simple say; "Integers are a fallacy". It doesn't make sense. I think I reached a paradox.


"You are wrong Jose, If integers doesn't exist, then 1+1=2 doesn't exist, you are breaking a simple rule called MATH".


I believe in GOD and I believe the entire universe is MATH. Even someone using math demostrated God exists. If I, Jose Pino, say: "Integers doesn't exists" then, it is equivalent to say "God doesn't exist".


I was wrong: Integers does exist. Stephen Hawkins is right. God created the integers. Integers are just part of the numbers and as fractions, they are almost impossible to define exactly where they are because there are infinite fractions around integers.


So, it ends there? That's it? No.


I find hard to understand that 1 (one) is composed by infinite fractions and the entire numbers are infinite. Great mathematicians had a hard time to understand and explain INFINITE. After thinking more about math and numbers, I found the problem are not the integers, the problem is: MATH is infinite, if I can't understand the nature of infinite, I will not be able to understand the nature of Integers.


I did a research, hours reading math books wasn't good enough for me to understand INFINITE, so I had to create my own theory about Infinite.


Let's review the graphical representation of whole numbers:


whole numbers


If a "unit" or integer is composed by "infinite fractions" then I believe infinite should reach a limit. As you can see, the graph shows 6 infinite units: from -3 to +3. Is that possible?


Yes. Integers are composed by Infinite fractions, so Infinite should reach an end.


my idea how to demostrate my theory about infinite. No book at the books store was able to confirm it, so, I had to find a way to demostrate it.


The image at the right is a paper that I used to find a way to demostrate my theory about the infinite. I started to think "where the infinite ends and starts again?"


Somehow, I had the idea that infinite numbers are represented by a circle, so the "whole numbers" are not longer a straight line. Here is my first theory about infinite numbers:



How is possible positive numbers just flip and converts on negative numbers? Well, that is not difficult to demostrate, even the magnetic pole of the earth will flip... just like that.


I can't compare the earth's magnetic field with my theory, but I can compare it with a computer. What happens when the binary system on a computer reaches the limit? It flips positive numbers to negative numbers and viceversa. If the computer process only 8 bits, it can count from -127 to +127. I believe positive numbers reach a limit and it becomes negative numbers, those numbers eventually goes back to zero.


Sounds interesting and may be feasible but there is a problem: If infinite goes back to zero, then infinite fractions may go back to zero and never reach any integer.


But think about this: If infinite fractions makes a "unit" or an integer AND infinite units or integers somewhow are equal to the starting point, then integers are somehow equivalent to zero.


"What's wrong with you Jose? 1 can't be equal to zero!"


Another paradox?


I don't like paradoxes. Somehow, even math can lead to paradoxes. I need to find a feasible way to demostrate the nature of infinite.


Well, here is my second theory:



Negative numbers and positive numbers are infinite and reaches back to zero. Positive numbers are negative numbers at the next sequence of numbers, consequently, negative numbers are positive numbers at the next sequence. I believe that is the nature of INFINITE on math.


If you look that spiral from the side, you will see a complete circle. It explain my first theory. Maybe you have the question: "How is possible there are many 0's (zeros) in your theory?"


Well, why not? An integer is a point where the fractions goes back to zero, but in another point. Even better; what if ZERO is not equal to ZERO in another point of the time? Whathever the answer is: Zero is just another point, as any other integer, of infinite numbers.


So, if I say: "Infinite numbers have an infinite numbers of ZERO in different points of time." it may be represented on this way:



Even TIME is infinite.


My second theory about infinite numbers may not make too much sense when I mention time on numbers, but I believe IF infinite fractions makes an Integer, THEN infinite integers makes an even bigger unit that human mind can't conceive, so I called it "time".


Why I believe the nature of infinite numbers is a "spring-shape" or spiral?


Because it fits perfectly when I try to explain infinite fractions. As you can see, the next drawing shows how integers are composed:



Each loop is composed of infinite fractions until it reaches the point "zero" and becomes an integer. Infinite integers or numbers are also represented as spiral.


This is a crude representation of infinite numbers:



Each loop have infinite loops of integers, so Infinite integers makes infinite units of infinite numbers and they are not named yet, or at least, no math book have a name for it. Not even mention something like that. Those "infinite units" makes another spiral for even infinite units of infinite units of infinite numbers.


The supporting data about my "theory of the infinite numbers" is the universe itself: A simple example is the earth, it rotates, translates and even travels thru the galaxy in spiral.


Infinite numbers doesn't end neither doesn't begin. There are points on the infinite that makes MATH possible and we know that points as Natural numbers, Whole numbers, Rational numbers and Real numbers.



Finally, If the lemniscate symbol is replaced with it may represent better the nature of infinite.


Tuesday, July 17, 2007


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