Hello Geodisic Why would the remaining 7/8s be infinite. The dividing up of infinity borders on nonsense in the first place, but it would be 8/8s of infinity that would be infinity, not a fraction thereof. Anyway don’t think you advanced the cause of explaining why 1/8 of infinity is infinity much at all. We should feel indebted to Phoenix 2634 for these definitions. The ray definition is a speculative definition, not a precise definition. The half infinite reference is acknowledgement that a ray is not infinite. A defined end is contradictory of an infinite line. Ray: in geometry a ray is usually taken to be a half infinite line with one of the two points A and B taken to be at infinity Line: ...An infinite line passing through points A and B ... ... A line segment terminating at these two points ... Infinity: An unbounded quantity greater than every real number... The infinite line (if it exists) passes through A and B. JR had his infinite line beginning at A. And infinity is an unbounded quantity. Proof of any such quantity we don’t have. In the mathematical world it can be speculated about as being greater than any real number as the definition says. In the physical world it is unlikely that there can be any such thing as an infinite quantity. Anyway, on these definitions safe to say that 7/8’s of infinity is not infinity. Can only be amused at fractions of infinity, particularly when those suspected of having university educations are the ones endorsing them. As this thread comes to its end, thanks university people for such wonderous amusement. Regards leeaus
Hello JR How can there be 8 infinities? Your definition of infinite volume was the positive values of x,y and z axes multiplied together. It did not account for all volume. Borders on the juvenile if you like. Infinity: An unbounded quantity greater than every real number How are you going to have eight of these. Regards leeaus
MacM, That was entirely my point. This is called proof by contradiction, by defining a rule and showing that it leads to a logical contradiction, you prove the rule is false. Take, for example, the proof that sqrt(2) is not a rational. Leeaus The remaining 7/8s would be infinite, because otherwise a finite 1/8 infinity plus 7/8 infinity would not be infinite. Two finite numbers cannot add up to an infinite number. Think about integers. There are an infinite number of integers, yet all but 19 of these integers (-9 to 9) have more than 1 digit. So how many digits are there in the set of positive integers? The answer is, of course, an infinite number.
Hello Geodisic Perhaps guilty of getting into Crisp’s semantic area. Infinity cannot be added to, subtracted from, multiplied or divided. Does that make the position clear when it comes to something like 8 x infinity. If infinity is being multiplied by 8, 8 infinites are implied as a beginning point. 8 infinities is a pure contradiction of terms. If 8 is being multiplied by infinity, then infinity must be a set or finite value. Otherwise the multiplication process cannot proceed. A set value of infinity is also a pure contradiction of terms. There are an infinite number of integers geodisic At the rudimentary level would what you mean by this is an integer follows an integer? Is that what you mean at a base level. This 8 x infinity stuff began with JRs pronouncement of an infinite cube. A cube always has side lengths with beginnings and ends. Thus there cannot be an infinite cube. Have little doubt that JR's proof of infinite distance is wrong. (sorry JR, the three dimensions got you). Regards leeaus
leeaus, How many real numbers are there in the interval [0,1] ? How many are there in the interval [0,2] ? Think about it. Bye! Crisp
Hello Crisp Am thinking about how may real numbers in your specified gaps 0f 0,1 and 0,2 as you ask. Are you also saying integers follow each other? The relevance to theories of the actual existence of infinite distance is what? regards leeaus
Think about the answer. First you think independently of eachother how many numbers there are in [0,1] and [0,2].... Then you relate those two numbers by saying "hey, the number of real numbers in [0,2] is twice that of in [0,1]". And if everything goes right, then you'll understand more about infinity. And if you already got the answer, think about the following: what is the difference between the limit of N going to 0 of 1/N and 1/N^2. Bye! Crisp
[0,1] [0,2] in both sets infinite lines are folded (as in a harmonica). They are the same long but one has more folds.
leeaus: <i>Anyway, on these definitions safe to say that 7/8’s of infinity is not infinity.</i> Let's follow your statement through to its logical conclusion. You say 7/8 infinity is not infinity, from which we must conclude that you think it is finite. But 7/8 infinity + 1/8 infinity = 8/8 infinity, which you agree is infinite. You said previously that no two finite numbers added together can give an infinite number. Since you now claim 7/8 infinity is finite, we must conclude that 1/8 infinity is infinite, because 7/8 + 1/8 = 1 and your agree infinity itself is infinite. But how can 1/8 infinity be infinite if 7/8 infinity is finite? 1/8 is less than 7/8. Your view is self-contradictory and, to put it bluntly, plain stupid. On your view, either: A. Both 1/7 infinity and 7/8 infinity are in fact finite, in which case adding them cannot give infinity and we are forced to conclude that infinity itself is finite OR B. 1/8 infinity is infinite and 7/8 infinity is finite, which is strange because it would seem obvious that 1/8 is less than 7/8. Then there's option C, for the real mathematicians: C. 1/8 infinity and 7/8 infinity are both themselves infinite. <i>Infinity cannot be added to, subtracted from, multiplied or divided. Does that make the position clear when it comes to something like 8 x infinity.</i> No, it obscures the truth, because it is false. The truth is that the rules of arithmetic are different for infinite quantities than they are for finite ones. I'm sure this is all completely over your head. Borders on the juvenile if you like.
Hello Crisp In the interval between 0 and 1 there is no real numbers. Between is your word. Once you move to a reciprocal of N, all considerations of integers are as a sub set of 1. Two lines are at right angles and you multiply their lengths together to ascertain the area that they enclose as a square. The lines are of infinite length as per your L + e stuff. JR told us that such a juxtaposition of infinite lines produces infinite area. (infinite X x infinite Y x infinite Z = infinite volume was the JR idea) Question. How do the mechanics of multiplication work when neither quantity being multiplied is of fixed in length. What is being pointed out is by mathematical definition area is finite. 3 x 3 is adding three to three to three. Infinity x infinity is adding what to what to what to what to what to what to what…………………………… Both area and volume are always mathematically finite. You cannot define them as infinite by their very natures can you. Both are enclosures, enclosures are not infinite. If you can’t process side length x side length, your end result is not area. Your side of things is infinite length extends in all directions from every point of space. This definition is ignorant of finite length. The non ignorant point of view is the length from point A in any direction is always different to length from point B in any direction. (There is distance between A and B.) Your definition says the same length (infinite length) extends from all points. What we debate when we discuss JR’s proof is whether or not finite length is real. If finite length is not real, your L + e proof can be considered. If finite length is real, different distances extend from all points of space. You shouldn’t have any argument with any of this, just a question of where finite length is real or not. If it is real, as always JRs proof is contradictory of its self. Regards leeaus
Hello JR. You misinterpret what was being said geodesic. Would was the word you missed. Read the post in the context of “if infinity existed it would be 8/8, not a fraction thereof.” Thus the A, B and C of your last post were decidedly irrelevant. Infinity was not being construed to be or defined as 8/8 of its self. Infinity cannot be added to, subtracted from, multiplied or divided. Does that make the position clear when it comes to something like 8 x infinity. The truth is that the rules of arithmetic are different for infinite quantities than they are for finite ones. Would you care to enlighten the universe as to the different rules. Regards leeaus
<i>Would you care to enlighten the universe as to the different rules.</i> Sure... In the following, f = a finite number, i = infinity. The rules are: i + f = i i - f = i i × f = i i / f = i i + i = i i - i = indeterminate i × i = i i / i = indeterminate There's a few extra ones involving zero (0): f × 0 = 0 f / 0 = i 0 / 0 = undefined i / 0 = undefined i *times; 0 = indeterminate
And i<sup>2</sup> = -1 Please Register or Log in to view the hidden image! Please Register or Log in to view the hidden image! Please Register or Log in to view the hidden image! Just kidding
Hello JR Thanks for your considered view of enlightenment. i + f = i If you achieve a larger quantity when you add a finite quantity to an infinite quantity, the first infinite quantity (the i of i + f) then is not infinity. The problem you always face is how this i becomes an f . It was an i, after your suspected due process it is an f as there is now a greater quantity than it. So on through the rest of your rules. They only make sense with an explanation of how an i ceases to be an i. Or how an f becomes an i in the case of subtraction. With no further explanation they are kite flying rules. With respect of your proof of the existence of infinite distance, you must show that infinity x infinity x infinity is infinity. How do you do the multiplying. It is just what it seems it would be to you at this stage of proceedings. The rules you have invented for the trades people are only assumptions without some sort of rational explanation. Regards leeaus
JR did not invent these rules. They are well known rules. In this thread, the only invention is the definition of infinity given by Leeaus, which is not consistent with the usual definition of infinity.
Leeaus Less talk of 'trades-people' if you please. What century are you in for God's sake? As an ex truck driver I'm perfectly capable of finding your argument totally incomprehensible.
Hello Canute and 1100f Sorry Canute. Trades people was a side reference that probably should not have been indulged in if it hit sensitivities. Your calling to God indicates you don't believe in the big bang. 1100f. Explanation of the rules is what is being sort. The inventor of the rules is not particular relevant. If they are more than assumptions they will have explanations. If you are privy to their explanations, your opportunity to present awaits. Is infinity odd or even. Both of these are finite as one follows the other. If it is trans integral infinity is as leeaus has specified. Regards leeaus
In the interval between 0 and 1 there is no real numbers. Between is your word. So 0.5 is not a real number according to you (it is in that interval). Or sqrt(2)/2 is not a real number ? also in that interval. Sorry, if you do not understand these concepts, it is completely useless to debate anything "advanced" such as infinity. Bye! Crisp
James R., Algebraically the above translates to: f = 0 x i That doesn't seem right since "f"in such case can be any number. Multiplying infinity by zero equals any finite number you want just seems bizzar. On the other hand I agree with the f/0 = i. So what rule(s) are involved that limit algebracially inverting the relationships. It just seems like saying a = b, b = c but a < > c. Knowing to believe only half of what you hear is a sign of intelligence. Knowing which half to believe will make you a genius.
