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Don Blazys

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About Don Blazys

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    La Crescenta, Ca.
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    security supervisor
  1. To: Megabrain, In my opinion, you have made some very astute (and courageous) observations. Quoting Megabrain: The great mathematician Kronicker once remarked: "The integers (meaning positive) were created by God, all else is the work of man." The ancients simply dismissed "negative numbers" as "folly" and viewed them as merely a superfluous "mirror image" of positive numbers. Negative numbers became accepted and adopted only as a matter of convenience and "convention", and as such have become "necessary". However, I agree that there is something quite "unnatu
  2. An Elementary Proof Of Both The Beal Conjecture And Fermat's Last Theorem. By: Don Blazys The Beal Conjecture can be stated as follows: For positive integers: [math]a, b, c, x, y, [/math] and [math]z[/math], if [math]a^x+b^y=c^z[/math], and [math]a, b[/math] and [math]c[/math] are co-prime, then[math]x, y[/math] and [math]z[/math] are not all greater than [math]2[/math]. Proof: Letting all variables herein represent positive integers, we form the equation: [math]c^z-b^y=a^x[/math].__________________________________________________________(1) Factoring (1) results in:
  3. The concept of "nothing" or "no thing" is simply inconcievable. By definition, there is no frame of reference by which it can be communicated or even experienced. It simply doesn't exist, and that fact/truth, in and of itself, forces existence into being and sustains all other concepts and perhaps even the physical universe as well. Don.
  4. To: Bignose, If I start a new thread on the BC, then can you post my proof in the very next post in LaTex so that other readers will find it easier to read? (I prefer versions #1 and #2) My website is perfectly safe to visit. It was created by the computer teachers at a Catholic high school. Don.
  5. To:Bignose, It might be a few days or so before I can post again as I have to go in for some tests and scans to determine the progress of my Alzheimers. If this is my final post here, then thanks for remaining interested throughout. Don.
  6. To: Bignose. You don't understand the difference detween meaningfull and trivial. Show me an example of a number other than a non-negative integer that does not require an "extra symbol built-in operation" and I will believe you! By your "logic", I can represent not just any number, but the entire universe using only the one symbol @. Utterly trivial. Don. To: D H The great mathematician Karl Gauss once remarked that: "Mathematics is largely a point of view." From my point of view, my "true colors", are "true mathematics". My topics, are both quite enter
  7. To: Bignose. My logic is not wrong. Yours is! When you say that "Pi" can be represented as the one symbol "1" in the base Pi system, you are hillariously wrong! In the base "Pi" system, the value "Pi" is represented as the two symbols "10". Besides, symbolizing "Pi" as "10" does not constitute an evaluation of "Pi". Pi is transendental and therefore can't be evaluated in any base. Pi can only be approximated. Thus, to take any "approximate number" as a base is to render even the most simple numbers impossible to evaluate exactly. For instance, how do you r
  8. To: Hadron Collider. Thanks, you made my day! Don. To: Bignose. No, it's not "utterly ridiculous"! The truth is that it is easy to write the number 10 using only one symbol. In the "base 12" or "duodecimal system", "10" would be written simply as "A" and "11" would be representet by "B". Thus, given a sufficiently large "base N" system, any non-negative integer whatsoever could be written using only one symbol. The non-negative integers are the only numbers that have this property! No other numbers do, or can! 10/3, (or in the "duodecimal system", A/3) is a perfectly go
  9. To: Bignose. Given the symbol X, if all we are told is that it represents a number, then what kind of number does it represent? Here is my answer to this question, and I hope it sheds some light on at least some of the difficulties that we encountered in this thread: Since the only clue we have is that X constitutes but one symbol, the only logical conclusion is that X must represent a non-negative integer, because all other numbers require more than one symbol in order to be properly and fully represented. In other words, the "intrinsic" value of an independent variable must b
  10. To: Bignose. This topic is about the properties of non-negative integers. Concepts such as "co-prime" require non-negative integers. 17^(1/2) and 17^(1/5) are not even rational numbers, much less non-negative integers! Thus, there is no way to define them as "co-prime"! My "cohesive terms" were specifically designed for use with non-negative integer variables. They allow us to solve hitherto intractable problems in "number theory" which is that branch of mathematics where we mathematicians focus primarily on the properties of non-negative integers. Thus, the log
  11. To:Bignose. Given the two equations: Ta^x+Tb^y=Tc^z and a^x+b^y=c^z, there is, of course, no value T which makes the first equation untrue when the second equation is true. The reason why: (T/T)a^x+(T/T)b^y=(T/T)c^z=a^x+b^y=c^z is wrong, is because it implies that the exponents x,y and z can all be greater than 2 after the "common factor" T has been cancelled. Take the simple numerical example: 6^3+3^3=3^5, and note that all three exponents are greater than 2. Also note that this equation contains the "common factor" 3^3=27. Now, extract and elimina
  12. To: Paganinio. Thanks. It is important! Moreover, it's new, and not in any books yet! I'm certain that it will lead to many other discoveries, so I hope you study it, and tell your friends and teachers about it. You see, if you love math, then you must love to explore, and "cohesive terms" open up a lot of "uncharted territory", because they are one of the few basic and fundamental constructs in math whose concequences and ramifications have yet to be fully and adequately explored. What could be more exiting than that? Happy exploring! Don.
  13. To: Josy. The Beal Conjecture says that if (T/T)a^x+(T/T)b^y=(T/T)c^z are co-prime, then x,y and z can not all be greater than 2. Now, the above equation must be co-prime because the greatest possible common factor T was cancelled, and we know that T must be the greatest possible common factor because if other common factors such as Q, R and S did exist, then they could all be multiplied together to form the product T= Q*R*S. I know that it's hard to believe, but had mathematicians learned how to represent and eliminate common factors properly to begin with, then problems such as the Beal Conj
  14. On The Proper Representation And Elimination Of Common Factors. By: Don Blazys. Our students are being taught that in order to render the terms in the equation: Ta^x+Tb^y=Tc^z relatively prime or "co-prime", we must first divide by T, then "cross out" the T's. However, doing so results in (T/T)a^x+(T/T)b^y=(T/T)c^z=a^x+b^y=c^z, which is wrong and inconsistent with both the "Beal Conjecture", and all observed results, because it falsely implies that x,y and z can all be greater than 2 after the common factor T has been cancelled and the terms are co-prime. Now the proper, correct and effective
  15. To: Bignose. Had you gone to my website, then you would have found that the variables in my equation represent non-negative integers. Any particular independent variable constitutes but one symbol and since non-negative integers are the only numbers that can possibly be represented using only one symbol, they are the most logical candidates for representation by independent variables. Thus, in order to be "perfectly rigorous", independent variables should represent non-negative integers only. All other numbers can then be derived by performing operations on those variables or the terms contain
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