James R., Posted by Leeaus: How then can L + e = be greater than L if L contains all positive values of x. If L + e is greater than L, then L + e may or may not contain all positive values of x. L then would not contain all values of x. Your proof by contradiction is a contradiction of your self. My post from above: ANS: You have already stated that L and e are finite numbers, hence L+e is the sum of finite numbers and that by definition cannot be infinite. Your claim therefor that the line extends to all postive x values is a false premis since e is a finite number greater than 0. L+e merely proves L was not the maximum finite number and adding e did not make it become infinite. Better yet is the recognition that there is no theoretical limit to finite numbers. You can always add +1, etc. Therefore logically it is easy to argue that infinity can not be a physical reality. ANS: Please respond to the issues raised. Your presentation is based on false premises. 1 - You cannot make claim that L includes all positive values of x since one can always add another. 2 - The only contridictions seems to be the basis of your presentation. There is a difference in not understanding a concept and not accepting it. I don't accept your explanation since it contains flawed assumptions. Knowing to believe only half of what you hear is a sign of intelligence. Knowing which half to believe will make you a genius.
Listen up, MacM (and leeaus), because I'm only going to step you through this once more. I will number each point, so you can clearly tell me which one you disagree with in future posts. <b>Aim</b> 1. To prove that the line containing all positive x values has infinite length. <b>Initial Assumptions</b> 2. There is a line containing all positive x values (including zero). 3. The line has a finite length L. 4. There is at least one real number e which is greater than zero. <b>Proof</b> 5. The x coordinate of any point on the line must lie between x=0 and x=L (by assumptions 2 and 3). 6. The value x=L+e is a positive value of x (from axioms of arithmetic and assumption 4) 7. The point at coordinate x=L+e is on the line (by statement 6 and assumption 2). <b>Identified contradiction</b> 8. Statement 7 contradicts statement 5. <b>Mathematical Reasoning</b> 9. Steps 5,6 and 7 are all valid inferences from the assumptions 2,3 and 4, and the axioms of arithmetic. 10. Since statements 8 and 9 are true, at least one of the assumptions 2,3 or 4 must be false. 11. Assumption 2 is obviously true, from other mathematical definitions (of "line" and "positive x values") which I can supply if necessary. 12. Assumption 4 is true by the definition of real numbers. <b>Conclusion</b> 13. Assumption 3 (the only one left) must be false. That completes the Proof of 1. ---------- Ok, MacM? Which step or steps is invalid here?
Hello Anders and JR. You define a line as finite then alter your terms of reference and define it as infinite. You missed the subtle point that any proving the line was not finite (which didn’t happen) did not make it infinite. L supposedly proven to be infinite. L + e is larger than L. If L + e is larger than L, obviously L is sub infinite. The proof by contradiction obviously contradicts its self with the unsubstantiated invention. All you possibly could be proving is that infinity can be approached but doesn’t exist. JR, don’t you understand that you are confusing negative numbers and an opposite direction of distance. What is your zero distance? If your proof of the existence of infinite distance was ever to mean anything, you would need to explain what zero distance is and how your invented infinite distance originated from zero distance. What you are saying is there is more length than 1 unit, what you need to chalk up is that length is never ending. Your are missing the point of what you are trying to do. Regards leeaus
leeaus None of my business but you really ought to try reading James's words properly. The fact that he had to redefine the line was the whole point of the post.
RE: JR If I substract from the line x-L L+e I will get a negative e. Is L (from point 2) long enough to be called infinite? (infinity-infinity should be 0)
Technically, James' proof doesn't include negative x coordinates, but I believe he did so for simplicity. A natural extension for his argument can be applied to the negative x values by essentially repeating it, with the appropriate sign changes. If you agree with the assumptions and the reasoning for his proof for positive x, then you should have no problem understanding how it would extend to negative numbers. Some things don't work out according to one's initial ideas in Mathematics, and the "∞ - ∞ = 0" falls into that category, for it is not true in general. A counterexample to your idea is as follows: lim <sub>n→∞</sub> x<sup>2</sup> = ∞ lim <sub>n→∞</sub> x = ∞ However, lim <sub>n→∞</sub> (x<sup>2</sup> - x) = ∞. Thus "∞ - ∞ = 0" is not necessarily true. Note: I can supply a formal definition of "a limit of a function is infinite" if you wish.
leeaus: You can continue waffling on if you like, but you haven't addressed my proof. Which step in my argument is wrong? (They are conveniently numbered for you above.)
James R., I find we must first discuss the faulty claims of your example. For it is they that create any contridiction and that contridction therefore doesn't implicate infinity. First your proposal is quite simular to asking the question "Have you stopped beating your wife?". Either a "Yes" or "No" answer will result in the person admitting to being a wife beater. It is a loaded question not based on supporting facts. That is what you have. Your assumptions: Aim 1. To prove that the line containing all positive x values has infinite length. ANS: OK if that were possible but it isn't Initial Assumptions 2. There is a line containing all positive x values (including zero). ANS: This is why it is not possible. Infinity is beyond numbers and there is no such thing as a line containing all possible positive x values because you can always add +n and have a bigger number. That is why infinity is beyond numbers and is not a unit of measure. You are trying to mix units. It is like adding yards and meters. It doesn't work because the units are not the same. You are claiming as your first physical assumption something that is prohibited by the very definition of infinity. 3. The line has a finite length L. ANS: No problem here 4. There is at least one real number e which is greater than zero. ANS: No problem here. Proof 5. The x coordinate of any point on the line must lie between x=0 and x=L (by assumptions 2 and 3). ANS: Problem here. As pointed out L can never represent a maximum number. 6. The value x=L+e is a positive value of x (from axioms of arithmetic and assumption 4) ANS: No problem here. x1=L and x2=L+e, still a finite length line. 7. The point at coordinate x=L+e is on the line (by statement 6 and assumption 2). ANS: No problem here. Although I think it is more of an extension of the line than "on the line" Identified contradiction 8. Statement 7 contradicts statement 5. ANS: Because it is based on false premisis. as stipulated in #2. Mathematical Reasoning ANS: Skipped since there is no reasoning using false premises. Conclusion 13. Assumption 3 (the only one left) must be false. ANS: The only thing false is the starting assumptions which voids the conclusion. That completes the Proof of 1. ---------- Ok, MacM? Which step or steps is invalid here? ANS: I believe I have #2. Infinity is not a unit of measure and you can not use numbers as a tool to prove something that has no numbers. Knowing to believe only half of what you hear is a sign of intelligence. Knowing which half to believe will make you a genius.
Re Dapthar My assumption was that an infinite set of Positive Numbers must include all positive numbers so that any number n and and also any (n + n) must be substractable from the "infinite" set of Positive Numbers (without coming to negative result).
Mathematics has shown that there are difference sizes of infinity. You can have larger and smaller infinities. For example, the set of integers is a smaller infinity than the set of reals. Yes it can, if there is no such thing as infinity. That is, the mathematics you are using contains no concept of infinity. James' proof shows that you can always add a positive integer to any maximum number, thereby creating a new maximum number. Hence by contradiction, there is no maximum number allowed. Ergo, a line can contain an infinite set of numbers.
thed, ANS: I am aware of that. But you can't switch horses mid-stream. Working with a particular set or basis of infinity then you are still stuck with the definition of infinity and James is violating its definiton and useful application by using numbers and using infinity as a measure of length. It can't be done. quote: -------------------------------------------------------------------------------- 5. The x coordinate of any point on the line must lie between x=0 and x=L (by assumptions 2 and 3). ANS: Problem here. As pointed out L can never represent a maximum number. -------------------------------------------------------------------------------- Yes it can, if there is no such thing as infinity. That is, the mathematics you are using contains no concept of infinity. James' proof shows that you can always add a positive integer to any maximum number, thereby creating a new maximum number. Hence by contradiction, there is no maximum number allowed. Ergo, a line can contain an infinite set of numbers. ANS: Your logic fails in this manner. The only maximum set of numbers is alway an infinite number of numbers, therefore L already = infinity and not a finite line. His bait and switch is an attempt to make infinity have a finite number represented as L. But L must already be infinity not finite as claimed. Knowing to believe only half of what you hear is a sign of intelligence. Knowing which half to believe will make you a genius.
Hello JR. Not waffling. You are. Your flaws are well pointed out by Macm and leeaus. Your proof might strangely mean something to you but means nothing to rational thinkers about the nature of space and the universe. (Assumption 2 is actually the false one.) Answer these questions if you wish. All are pertinent to the proof that isn’t. Are all positive values of x an infinite or finite amount of values? Is L + e a greater distance than L? Is 0 to e a measure of distance? Born when you were but with a perfect body that never dies, would you live to an infinite or finite age? What is the proof that proof by contradiction is proof? What you do not address (mainly) is the distance that exists before zero distance. If you could come out of unwarranted self congratulatory mode and address some of the points put to you that shows the flaws in your logic, you would see that you have not proven that infinite distance exists. You should read more carefully the flaws already pointed out to you. You are in finite space with a false belief in infinte space and we are here to help. Regards leeaus
leeaus: i said before that site policy forbids crackpot responses on legitimate threads. well i think this thread has been extremely successfully hijacked by the crackpots. she s all yours! enjoy.
leeaus: why not build upon your alternative logic new and better mathematics and physics to adress the flaws in modern science. otherwise, an alternative logic is just useless, or just plain "waffling". MacM: "But L must already be infinity not finite as claimed." If you read what James has been writing, you will notice that the proof shows precisely this. I.e, the proof shows that the assumption that L is finite is false. Doesn't seem like you're really paying attention. Please Register or Log in to view the hidden image!
I am a rational thinker, I perfectly understand his proof. Are all positive values of x an infinite or finite amount of values? It is not finite Is L + e a greater distance than L? If L is a distance (then it is a positive number) and e is a distance, then L+e is greater than L Is 0 to e a measure of distance? A distance is something you measure between 2 points on the line. Born when you were but with a perfect body that never dies, would you live to an infinite or finite age? Infinite. What is the proof that proof by contradiction is proof? And What is the proof that a proof is a proof? And if you give me a proof that a proof is a proof, what is the proof that this proof is a proof?
Hello Lethe Tend to agree, you have to be a crackpot to bother with JRs proof of infinite distance. Hello AndersHermasson. Not presenting an alternative logic. Just showing that proof of the existence of infinite distance does not exist. This thread began with a question of whether space is finite or infinite. Hello 1100f What is the infinite value of x? If L + e is greater than L, to a rational thinker L is proven finite length. There is a length greater than L. Therefore L is finite. Born when you were but with a perfect body that never dies, would you live to an infinite or finite age? Infinite The answer you give is wrong 1100f. Whilst you live on your age will always be describable by a finite number. It began at 1 and so on. There is also the time before you were born. Only dapthar has attempted to address the question of the distance before zero distance. Continued with the confusion between negative numbers and an opposite direction of distance, though. So all rubbish these attempts to prove that infinite distance exists. No one has it in their mind as to what infinite distance is. All anyone has done is say the finite beginning at one end is never ending. No-one has described what infinite distance is with both ends open. Until you can do that forget the one open end nonsense, girls and boys. Infinite distance has both ends open. Otherwise it is not infinite. Grow up, mature, think hard in opposite directions at the same time. With effort and endeavour you will get to a true moment of reckoning about whether space is finite or infinite. All the best and Regards leeaus
leeaus, We are in agreement on this. You can add to this view that such an infinite line cannot even be cut in half theoretically and hence it is impossible to subtract one half of an infinite line from the other to get zero. An infinite line has no mid point from which to cut by definition. At the same time one must grant James and the others this much and no more. An infinite line severed anywhere along the line results in two infinite lines by definition since infinity cannot be divided into finite lengths. This fact supports the arguement that an infinite line with one end open can be infinite. This proves four things: 1 - Infinity by definition is its own indeterminent paradox. 2 - Such other arbitrary arguements trying to prove infinity are equally paradoxial and can be both false and true at the same time just as most mathematical assumptions about infinity are. That being the case infinity and its assumptions, by definition, are also proof that infinity doesn't exist. Another paradox in of itself. 3 - Infinity is not a number, which by definition must be finite, but is a mere physically impossible concept useful to man only in mathematics and not physical reality and those that claim infinity (including infinity as physical reality) should be rejected outright as being false concepts or misapplication of concepts which are purely mathematical without a physical cause. 4 - Our comprehension of the issue appears better founded than those claiming expertise and that call us Crackpots. Please Register or Log in to view the hidden image! Knowing to believe only half of what you hear is a sign of intelligence. Knowing which half to believe will make you a genius.
RE:MacM from my earlier entry page 6. It you cut Lx in two Lx1 and Lx2 they will be both eliminated if you reverse the direction of length - they are not infinite any more.
ProCop, RE:MacM quote: -------------------------------------------------------------------------------- At the same time one must grant James and the others this much and no more. An infinite line severed anywhere along the line results in two infinite lines by definition since infinity cannot be divided into finite lengths. -------------------------------------------------------------------------------- from my earlier entry page 6. quote: -------------------------------------------------------------------------------- A Line La which stared at a point A and approaches infinity is different long from a Line Lx which started at no point. If you reverse the process of approaching the infinity of both lines La will come back to a point A and La will be eliminated. Only the Lx is truely infinite - (it has no end and cannot be eliminated). -------------------------------------------------------------------------------- It you cut Lx in two Lx1 and Lx2 they will be both eliminated if you reverse the direction of length - they are not infinite any more. ANS: I accept the arguement but only because infinity is not a length and regardless of what you do to it (cut it anywhere) the pieces so cut are equal i.e. infinite pieces. But that is because infinity is not a number and cannot be used as a measure of length and you are adding, subtracting, multiplying and dividing a definition not a physical enity. Because of that cutting a true endless infinite line results in TWO infinitities equal in every respect regardles if you move the point of the cut left or right along the line. It can clearly be seen that by definition infinity is not a fixed quanity subject to numerical manipulation since the proportions are invariant to physical (mathematical manipulation). Knowing to believe only half of what you hear is a sign of intelligence. Knowing which half to believe will make you a genius.
