Josan said:Please don't bring reality into this. We're talking about mathematics, not reality =P
I see. My mistake.
0 divided by (1,2,...,n) will always be zero.
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Josan said:Please don't bring reality into this. We're talking about mathematics, not reality =P
JustBusiness17 said:This thought originally came out of the idea that "everything came from nothing" which seems to be a central debate no matter what level of regression your beliefs allow you to envision. This topic is probably better categorized under philosophy, although I wanted some professional mathematicians to tell me where I might be wrong...
So, without necessarily assuming there was a "beginning" to anything, I'm starting this thought experiment at zero. Rather than thinking of zero in its traditional sense (that of being nothing) we can actually think of zero as being infinitely vast in its nothingness. You might assume that an infinity of nothingness is still nothing, although that assumption overlooks the incomprehensible nature of infinity. Georg Cantor was one of the first to really embrace the concept of infinity for what it really is, which is limitlessness within limitlessness taken to infinity. It's a difficult concept to struggle with which is probably why Cantor went insane...
A concept that I can't seem to shake (and if you detect a flaw, please elaborate) is the idea that zero divide by infinity allows for all possibilities. Consider 0/1=0, 0/2=0 ... , all the way up to 0/∞=0. Regardless of the denominator, 0 divided by anything is still zero. But, taking into consideration the limitless nature of infinity, zero divided by infinity creates limitless possibilities for something within nothing.
JustBusiness17 said:I bolster this point with the idea that physicists speculate that sum over all energy within our own universe is actually equal to zero. The positive balances the negative which makes us a null equation. If you take the nothingness of our universe and insert it into one of the infinite fractions of zero, the equation still balances to zero.
JustBusiness17 said:Just so that people can wrap their heads around this concept, I'm suggesting that something may be possible when you take 0/∞/∞/∞/∞/∞/∞/∞/∞/∞..../∞. Zero may be nothing, but when examined on an infinitely small scale, there is always the possibility for something...
(Please put this idea to rest because it's been bothering me for a while...)
Josan said:lrkun said:The symbol zero represents that which is absent.
Not neccesairly, it represents the only real number that is neither negative nor positive. (And we are talking about the number zero. It is, after all, a number, don't try to pretend otherwise)
Multiplication:
| 1 | x | x+1
-------------------------
1 | 1 | x | x+1
x | x | x+1 | 1
x+1| x+1 | 1 | x
Josan said:lrkun said:Nothing can't be divided by something. To illustrate:
0/a or 0 divided by A. In reality it looks like this. divided by A. The thing before divided by is not there.
Please don't bring reality into this. We're talking about mathematics, not reality =P
<i>
</i>1. 1010001001000101001.......
2.0100101110111011110........
3. 0100100100101000101.......
.
.
.
.
<i>
</i>1234567898789.......
2345345656777.......
13242354656488.......
12233445566778......
1234356667878999..
3265789000989898...
Zetetic said:You seem to be confused. You see, a mathematical system has no internal semantics, only internal rules. As long as you follow the rules, the meaning of the outcome doesn't matter. Mathematical models only adopt significance when correctly applied to a phenomenon that follows the rules sufficiently closely for predictive purposes.
Zetetic said:You are correct in deducing this, however; this should indicate to you that your thoughts about how random mathematical rule sets (they might not seem random to you if you've only had exposure to calculus) might say something about reality are in fact similar in nature to astrology.
No! You have made the mistake to try and do math with apples, there is no such thing as apples in math. Zero is by definition an number a such that for any number b: a+b=b.That is it. The fact that you can establish a paralel between the proprety of addition to counting apples and zero as having no apples has absolutly no effect in math. There is an ent that represets nothing in math, a.k.a. Void, it is not a number but it has mindfucking propreties in set theory.lrkun said:The symbol zero represents that which is absent.
0 nothing 1 something.
I have 5 apples. Take away 5, how many are left? 0 = none are left.
0 alone is nothing.
10 - no longer nothing, this represents 10 or to follow my previous example, 10 apples.
Master_Ghost_Knight said:No! You have made the mistake to try and do math with apples, there is no such thing as apples in math. Zero is by definition an number a such that for any number b: a+b=b.That is it. The fact that you can establish a paralel between the proprety of addition to counting apples and zero as having no apples has absolutly no effect in math. There is an ent that represets nothing in math, a.k.a. Void, it is not a number but it has mindfucking propreties in set theory.
What do you mean?lrkun said:Zero divided by any number is equal to zero. That is math. Now with respect to your point, it does not make sense. I am not in anyway saying otherswise.
Master_Ghost_Knight said:What do you mean?
Re-reading your post, I can atribute a second interpretation where you might wanted to introduce a graphical ilustration, I can see how you can object to that.
Anyways a graphical ilustration is not exactly how we show 0/n=0 with n=/=0 even tough is not a bad way to go an intuition of it.
Just on a side note, the proof goes like this: a division in fact doesn't exist in math as a full operand 1/b in fact means a number c such that for any b not zero c*b=1 and we call c = 1/b. So all we have to prove that 0*c=0 for any real c.
And now it is easy using the axioms:
1. The sum identity a+0=a, from here 0+0=0
2. The distributive proprety a*(b+c)=a*b+a*c
3. And finaly the existance of the simetric, for any "a" there is "b" such that a+b=0, and we call b = -a
c*0=c*(0+0)=c*0+c*0 <=>c*0+c*0-c*0=c*0-c*0 <=> c*0=0
Josan said:I am well aware of this, did I indicate otherwise? Perhaps I did, in that case I apologize, I wrote my comment in haste. I was just trying to clearify that 0 is a number, just like any other number. This might seem obvious to anyone who knows math, but I have on many occasions had tireing discussion only to find out that it is the misconception that 0 is a concept, not a number that is the problem. All I was trying to specify was that 0 is a number, to be exact the only real number that is neither negative, nor positive. I realize now tthat I phrasphed myself as if that is the sole definition of the number 0, which I never meant to imply, I was simply pointing out one of it's properties as a juxtaposition to the statement that 0 is solely a representation of nothing.
Josan said:Okey now, this is not what I said at all. Again, I was simply trying to point out, that you can't make arguments based on reality when talking about math. I have never stated that the rules are random, nor do I consider them to be. And for your information, I have taken several courses in calculus, thanks for assuming otherwise.
Josan said:So in summary. My comments were made in haste and were intended to add a slight clarity to his argument, as well as an attempt at some humor (which obviously failed). However, I think you misrepresent my comments entirely.
Other than that. Awesome post.
Zetetic said:I found your post confusing and hard to follow
Zetetic said:I saw the specific phrase speaking about infinite possibilities and infinity being limitless, and deduced that it was likley that you were using a layman's definition of infinity and conflating it with mathematical definitions of infinity and drawing confusing conclusions. It appears that it is not the concept that confuses you or frustrates you, but rather trying to teach it to people who have varied layman's accounts of various concepts that they are not willing to suspend for the sake of understanding you. This might be partially because you are inexperienced at teaching, and likely partly because of general refusal to learn. Many people are more interested in appearing competent than in understanding what is being said. I have trouble with this, we all do, and our confused notions tht we cling to often get in the way of communication.
I would suggest explaining 0 historically, perhaps by bringing up Fibbonacci, and characterizing 0 as 'mathematical', rather than 'colloquial' or 'lay' 'zero'. I suggest not defining colloquial zero, as it represents what ever confused notion that is held by the person happens to be. Once you have established that mathematical 0 is not what they have encountered outside of mathematics, they might lose their biases. Then you must illustrate how zero is used and what rules it has. Make it clear that 0 is part of an abstract game, and that their existential considerations (if these are the problem you generally run into) are unrelated to it. They will likely admit that this is not what they were talking about and stop using the metaphor of 0 representing 'nothingness'.
You might make it clear that the formal mathematical use diverges from what they are driving at, and that their thoughts are strictly non-mathematical. 0 as a mathematical entity is clearly defined. When applied to reality, it is only defined with respect to an object that has to be specified prior to it's application. I only use it in front of a noun. There is zero charge, there are zero eggs, there are zero molecules. They are making a categorical mistake. They apply zero globally when only local applications make sense. Their problem is not realizing that zero requires a noun. Once they can specify a noun to which they are applying zero to, then they will no longer be confused.
Zetetic said:If you noticed, I suggested that you have only had exposure to calculus, but not too much higher mathematics. I never indicated that you have not taken calculus. That aside, I actually should not have quoted your post, I thought it was something written by JustBuisness17 because I had been up all night (for unrelated reasons) and was writing an exhaustively long post with lots of detail and lost track of who I was quoting.. Most of what came after your post was not directed at you so much as it was directed at justBuisiness17. I, mistaking the quote for another one of his, used it to parlay in to my further points about mathematical infinity.
Zetetic said:As you now know, I was confused! Thank you for the compliment! Unless you are being sarcastic!
Josan said:Zetetic said:I found your post confusing and hard to follow
My bad. I have an easier time explaining challenging concepts to people in person, when I can see their response on a word-by-word basis. Also, English is not my native language, so I find discussing physics and math difficult in English, as I tend to innocently mix up phrases that sound similar, but are completely different!