This is about as retarded as it gets. A mathematical proof of integer relations is different from measuring.
You absolutely, positively did no such thing. Your non-recognition of "real" as an adjective in reference to numbers and this ludicrous statement leads me to believe that you've actually not been exposed to mathematical proofs much. Here are two uttely destroying problems with your "proof": 1) You test combinations of side lengths ranging from 1 to 10000. That leaves infinitely many cases unaccounted for. 2) You use numerical approximations of acos and pi (yes, you do), meaning that your test is not even to be trusted for the incredibly few instances you've tried. Furthermore you compare floating point numbers (the equality tests) after doing approximate calculations, something every CS student learns the hard way. This sums to you having proved exactly nothing at all. That's not a definition. It's a (true) inequality. Depending on the sofistication of your calculator, it will most probably also tell you that (0.000000001)^100 = 0. Do you think this is true, too?
Funkstar, you clearly missed the context of everything here, QQ was dividing 360 by numbers. He was trying to show how 360 was a factor of every integer. schmoe took this to mean that angles can only be divided by integers, which is not true. An angle can be divided by any number you want. When you start dividing by numbers less than 1, it is the same as multiplying by the inverse of that number which would be greater than 1. So when 0 is included in the following list, division by 0 must be approached as the limit of x as x->0+ of 360/x. What is so difficult here? As QQ posted it:
No. Even this is wrong. And we're not doing approximate numbers. This is still wrong. If we're talking reals, x/0 is still undefined. You're. Wrong.
Sorry funkstar, but your blather has no relevance here. I already said that it was not a formal proof. I know the difference between a formal proof and what I did - I've taken plenty of high level math courses. I already stated that calling it a "proof" was a misnomer.
YOU ARE NOT USING APPROXIMATE NUMBERS. I am. You are only working with integers, I am not. I realize you are a mathematician and therefore you jumped all over this thread to strut your stuff, but you are simply wrong. As a mathematician, I suspect you have no concept of degree of accuracy and that almost all numbers used in any real world calculation is an approximation with the exception of "counted" quantities. If you have 5 apples in your hands - that is not an approximation. But if you were to weigh those same 5 apples on a scale, that weight will always be approximate.
I know perfectly well how this came about. He didn't. He took exception to your claim that 360/0 is infinity, because it isn't. It's undefined. The difficulty is that it's just not true. You can't even use the limit lim x -> 0 360/x != infinity because lim x -> 0+ 360/x != lim x -> 0- 360/x and both are limits of 360/x when x goes to zero. That's all there's to it. 360/0 is not infinity.
for integers. I've never claimed otherwise. And it was not myself who claimed 360/0 = infinity, it was superluminal. And it was superluminal that he took exception to, not me. Get your facts straight if you want to claim that you know how all this came about. Your post below is evidence that you have no clue how it all came about: See, you are still trying to approach 0 from the negative end! HA! Nice try though, it truely is the strongest argument you have going for you. Keep hitting on it some more. Maybe I'll give up telling you that the negative end is irrelevant for the purpose brought up in this thread. Probably not though.
It's not even a good approximate test. You make the rookie mistake of comparing floating point numbers.
what is 360/N where N=.0005 +/- .0005 degree of accuracy? See how measured quantities cannot be arbitrarily defined as real? I suspect your answer will be no because you are a mathematician.
It was good enough for the accurarcy of MATLAB and the limit of 10,000 that I used. I understand when results become inaccurate because of computer limitations. In fact, MATLAB would have warned me of any such results with warning messages. I had that covered Please Register or Log in to view the hidden image!
Holy crap, you really don't know what a "real" is, do you? "I've taken plenty of high level math courses." Yeah. Sure you have.
That is entirely my point. As a mathematician, you have no conceptual clue as to why N/0 is infinity when you are talking about real world numbers. Again, integers clearly do not apply.
Who "measured" anything in this thread? Were you peeking in QQ's window as he played with cardboard cutouts of triangles? I guess I'm schmoe, but I didn't do what you're claiming here. My hope of restricting N/0 to being integers was to divert the course from your insane ramblings about approximations that doesn't appear to have any relevance here. Even by your own "measuring" rantings, what is 0 in QQ's post measuring? care to explain how it's somehow not an integer? Do you think there are 360 degrees in a circle or is it 360+/- 0.01?
Sorry for making your nickname German - it is just my nature. I realize you don't believe it to have any relevance, but it is relevant. What else can I say? Like I said before, he only showed the result of the integer divisions - why does that make any angle you divide have to be divided by an integer? The number of degrees in a circle is defined as 360. Dividing this angle by 1/2 is the same as multiplying it by 2. Dividing by 1/100 is the same as multiplying by 100. Dividing by 1/10000 is the same as multiplying by 10000. See the trend? It goes to infinity. Holy shit, imagine that.
Good! Now is division defined for reals? Yes, it is, except when the second operand is zero. Well, does it at least have a unique limit, that we can use instead? No, it does not. What does this mean? It means that 360/0 is not infinity. Now, even if we extend the reals to include +/- infinity, it still doesn't make 360/0 = +infinity.
How about you answer my question: what is 360/N where N=.0005 +/- .0005 degree of accuracy? Do you know how to do such a calculation? I know I had to do such mundane calculations in chemistry lab.
