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Asterisk Propernoun

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About Asterisk Propernoun

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    Pure Mathematics
  1. So, I've been debating with someone over the existence of god, and we eventually reached the subject of intelligent design. This is his argument: Being someone who has no special interest in biology, I don't know how to refute this. What do you guys think? In order to prevent redundancy, I'll type down the arguments I've made so far: I've shown him Niel deGrasse Tyson's video on stupid design and Richard Dawkin's video on a nerve in a giraffe to show that a competent engineer (an intelligent designer) would never have created nature the way it is. I've also used Richard Dawkin's video (specific time here) to show how evolution can explain what intelligent design can't. I've given Bill Nye's example of a fossil prediction to show that evolution is accepted not because of dogma, but because it's reliable.
  2. I have several retorts: 1. This is more bullying than it is formal debate, so I wouldn't even bother with it. 2. Just because a person hasn't done something doesn't mean they won't. I had a D average in my algebra classes last year, but I worked hard over the Summer and now my current overall grade in geometry is a 101.7 (it's over 100 because the teacher offers test bonuses). 3. If gold is more valuable than silver, then silver is worthless. See the fallacy?
  3. So what you're saying is that I can rotate the complex plane 180o along it's real axis and make it to where -i is on top and i is on the bottom without consequence? This would make sense to me, seeing as it wouldn't lead to -i=i since, not only would it make positives into negatives, but it would also at the same time make negatives into positives, thus maintaining a difference.
  4. I think you all are misunderstanding what I'm trying to say: I am not trying to say that -2=2, because 2 isn't soley defined as being the solution to a2=4. However, my friend from the other day told me that i is soley defined by i2=-1, meaning that -i=i because they're both solutions to a2=-1, and this is confusing me because, like I've shown, that would mean you could substitute i with -i when adding i and i together, thus turning it into i minus i without changing the end result, which is 2i. The problem I'm having is understanding how i is defined. Was my friend wrong in saying that the only thing that defines i is i2=-1? Was he right about that, yet wrong when he said that this leads to i=-i? Was I wrong when I said that this opens up the possibility for i-i=2i? I honestly don't know. I'm confused. EDIT: At Acme. I'm not trying to solve any specific equations. For now, I'm just trying to understand and get used to the concept.
  5. That much I get, but I was told that, since i is solely defined by i2=-1, that there's no difference between i and -i because you can square the negative version of a number and get the same answer: 22=4=(-22)
  6. So, I'm having problems with understanding imaginary units. My friend told me that -i=i, but I confused him when I showed him this: -i=i 2i=i+i=i+(-i)=i-i i-i=2i? I must be missing something...
  7. I occasionally make posts on this thread to ask questions, but most of the time I'm on a different forum which uses the same Invision Power Services software as this forum (although the versions may be different). The other forum I'm on has three separate themes that can be changed with a tiny button on the bottom of the main page, and those three themes are normal, mobile, and IP.Board (default). The IP.Board theme, in all honesty, looks almost exactly like the theme of scienceforums.net. What I'm suggesting is that we should get some ideas going in this thread so we can give this forum it's own little unique touch.
  8. (pq+((p-q)/2)2)0.5±(p-q)/2=p&q I think that there's a consistent method to prove whenever statements such as this are true or not. Does anyone here know what that method is?
  9. Let's say that there's a function whose limit is zero as the function approaches infinity. Would I be justified in saying that, if I put infinity in the function, that the answer would be zero?
  10. Hey, I have plans on posting this in another forum, and I would like to have my work checked before I do so. Here it is:
  11. I once read a thread with a post in it saying "Everything is possible, unless it isn't." I read another thread just recently with the post "Hypothesis are assumed true until they're proven wrong." I'm seeing flaws in this logic. So if I were to create a hypothesis that was extremely unlikely, yet impossible to prove/disprove, we should all just assume it's true? For instance, how would you disprove my hypothesis that, in the center of every star is not nuclear fusion but is instead a dragon radiating firebreath in all directions? You may say this dragon couldn't ever exist because <insert long explanation here>, but then I'll make another hypothesis as to why it is possible, and a hypothesis that explains why the last hypothesis is possible, and so on. Before you know it, I've created an entire web of assumptions that explains the universe in ways that cannot be proven or disproven. I am seeing some serious problems with the idea that everything is to be assumed true until it's proven false. Care to help me out of this pit of confusion?
  12. This was just a little expirement that went on inside my head while I was on one of my walks. It seemed interesting at the time, so I'm going to share it with you. We have an x axis that represents all real numbers, and a y axis that represets all imaginary numbers, i^2=-1. The idea of a whole-nother number line sounds fascinating; and to some, literally unbelievable. However, dispite some people's disbelief, the imaginary number line and the complex plane is perfectly sound from a mathematical standpoint. If we managed to solve something impossible like -1^0.5, then maybe we can do the same with another impossible function like a/0. A person (I can't remember who) once said that smart people learn through trial and error, while smarter people learn through other people's trial and error. So, I started out by showing the marks on the z axis as -1(1/0), 0(1/0), 1(1/0), and so on. However, I quickly realized that this would simplify to -1/0, 0/0, 1/0, and so on. Well, I made a third dimension. Now the questions were what good was it and what are it's properties? Well, let's start by comparing 1/0 to -1^0.5. A few people who don't accept the complex plain may argue that -1^0.5 just equals 1. However, when you find the square root of a number, you should be able to reverse the process by squaring. 25^0.5=5 5^2=25 You cannot do this with a real number only argument to -1^0.5. -1^0.5=1 1^2=1 If the person you were arguing debating with was desprate to hold on to their claims, they may say that 1^2= +/- 1. Please, tell me what's wrong with this picture: 1*1=-1 So, I concluded in my head that, if you wanted -1^0.5 to work, you needed to use the imaginary unit i. I am now going to compare the problems with using real numbers for -1^0.5 with 1/0. Again, you should be able to reverse what you've done. 10/5=2 2*5=10 And again, this won't work if 1/0=, say, 0. This was something I didn't take in to consideration on my first attempt to divide by zero. 10/0=0 0*0=0 The question now is, can the third dimension I added fix this? I believe so. However, it may be difficult to wrap your head around the solution. 10/0= the tenth place on my axis. For now, let's just call that place 10g. 10g*0=10 So when you multiply g by 0, you get 1? Well, when you think about it; yea, why not? Wouldn't you agree that *0 cancels out /0 the same way *5 cancels out /5? Getting a nonzero number through multiplication by zero is no less believable than saying you multiplied two of the same signs together and got a negative number. Another problem a mathematician on this forum told me was that, if we were to make it where any number divided by zero equaled the same number, then that opens up the possibility for any number to equal any other number: 2/0=0 3/0=0 Therefore, 2=3 This doesn't happen with my idea. 2/0=2g 3/0=3g Therefore, 2=/=3. So, is this perfectly sound like the complex plain, or does it have problems?
  13. I decided to collect some data so I can show you what I mean. The one-time pad generator I used. The python script I used will be in an attached file. The script will include the keys I used. The script's output: 1. a: 100 b: 122 c: 97 d: 83 e: 104 f: 104 g: 117 h: 100 i: 105 j: 87 k: 93 l: 112 m: 88 n: 76 o: 118 p: 113 q: 107 r: 105 s: 94 t: 96 u: 99 v: 90 w: 99 x: 86 y: 89 z: 116 2. a: 85 b: 129 c: 102 d: 113 e: 84 f: 93 g: 116 h: 91 i: 120 j: 98 k: 99 l: 105 m: 101 n: 96 o: 99 p: 101 q: 100 r: 103 s: 84 t: 111 u: 94 v: 92 w: 82 x: 103 y: 105 z: 94 3. a: 90 b: 119 c: 94 d: 89 e: 97 f: 102 g: 78 h: 123 i: 118 j: 104 k: 93 l: 92 m: 99 n: 98 o: 106 p: 95 q: 107 r: 108 s: 96 t: 104 u: 117 v: 102 w: 98 x: 111 y: 87 z: 73 4. a: 104 b: 105 c: 93 d: 110 e: 89 f: 99 g: 92 h: 87 i: 93 j: 105 k: 98 l: 99 m: 97 n: 121 o: 104 p: 103 q: 103 r: 100 s: 98 t: 100 u: 110 v: 94 w: 84 x: 115 y: 98 z: 99 5. a: 112 b: 90 c: 101 d: 98 e: 103 f: 113 g: 83 h: 96 i: 102 j: 99 k: 94 l: 100 m: 104 n: 99 o: 86 p: 80 q: 95 r: 112 s: 113 t: 107 u: 96 v: 96 w: 126 x: 107 y: 92 z: 96 6. a: 119 b: 100 c: 97 d: 85 e: 94 f: 107 g: 103 h: 98 i: 100 j: 89 k: 90 l: 120 m: 102 n: 107 o: 104 p: 81 q: 99 r: 108 s: 101 t: 92 u: 96 v: 94 w: 117 x: 98 y: 115 z: 84 7. a: 94 b: 84 c: 94 d: 87 e: 98 f: 90 g: 117 h: 93 i: 110 j: 125 k: 85 l: 98 m: 94 n: 103 o: 125 p: 129 q: 105 r: 91 s: 95 t: 103 u: 90 v: 90 w: 107 x: 90 y: 113 z: 90 8. a: 85 b: 105 c: 105 d: 88 e: 99 f: 89 g: 99 h: 111 i: 93 j: 104 k: 100 l: 100 m: 113 n: 101 o: 105 p: 107 q: 74 r: 107 s: 102 t: 101 u: 95 v: 106 w: 86 x: 117 y: 106 z: 102 9. a: 98 b: 118 c: 98 d: 80 e: 108 f: 104 g: 109 h: 95 i: 94 j: 82 k: 103 l: 100 m: 103 n: 88 o: 96 p: 109 q: 110 r: 104 s: 104 t: 84 u: 102 v: 104 w: 107 x: 101 y: 110 z: 89 10. a: 103 b: 92 c: 90 d: 105 e: 98 f: 121 g: 104 h: 104 i: 111 j: 103 k: 103 l: 108 m: 103 n: 107 o: 99 p: 87 q: 110 r: 94 s: 96 t: 95 u: 100 v: 100 w: 86 x: 94 y: 81 z: 106 The ten keys I tested where all 2600 letters long. It looks like I was correct in thinking that each of the letters would tend towards 100 since 2600/26=100, and each letter in the key had an equal chance of occurring. Of course, I could've just used a generator that wasn't any good, but I believe this counts for at least something. EDIT: Wait a minute. Okay, I see what John Cuthber means. I may be correct in my statement, but something important to realize is that there are more possible combinations of letters when they're equal in quantity. When the key is basically a Julius Caesar cipher and all of the letters are the same, there are only 26 different possibilities. However, a key that's 2600 letters long and has 100 of each letter may have thousands of possible combinations. Although, on average, the key will have an equal amount of each letter, there are more equal letter combinations than any other combination that isn't equal. So, although my observation was correct, it didn't have the effect on one-time pad cryptanalysis that I thought it had. Counter.txt
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