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You are not logged in. #26 20121010 23:13:25
Re: Symbol for Infinitesimal?Hi;
Where is the √2 on the number line? Is it here 1.414.? Or here 1.414213562373095?
3 is not 3 apples or 3 canaries or 3 battleships. It is just defined as the integer following 2. In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #27 20121011 06:56:16
Re: Symbol for Infinitesimal?
Okay, so I'm curious just how much we agree on this...
I might have been inclined to agree with that myself, except for the last part, "zero over infinity." I do not know quite what you mean by that...but yet again, you seem to be talking about something else. I will give a further example later on in my explanation, but for now will just say, that does not make any sense mathematically.
Again, I have a problem with the last thing you wrote, "Mathematically, one over infinity." I don't know how to emphasize that idea is no longer valid. If you need proof on that, I can lead you to a number of websites my brother had to take me to to drill that in my head. This is an OLDER idea of what was thought to be an infinitesimal back then, and is NO longer accepted. Infinity can NOT be used as such and I feel like if you understood what infinity was, you'd understand WHY this does not make sense.
I am not 100% sure what you mean by all of this, mostly the part thats says, "It's what we can deal with, see, touch, measure, conceive of, etc." Besides for maybe the conceiving part, I don't think I can fully agree with all that. On top of that, just like in my last example, you can not use infinity like that with normal numbers...I do not know how I can stress this anymore. This is similar to 1/∞, but instead, now your replacing 1 with x. This is wrong, I already explained that infinity is a different concept, just like in my earlier example...
You just can not do it. Granted infinity might not be the same as +, but by the WAY you are using it, it still comes to the same idea.
Well again, this is YOUR idea that you have been trying to argue the whole time. Yet you seem to mostly be repeating the same thing more or less. I don't really even feel I need to put yet another argument against this, but for arguments sake, I will. Now so I'm not repeating the same old stuff, let me first talk about this. Yet again, another fraction that makes no sense with the use of infinity. Now, just assuming that infinity is a number (breaking the rules here), wouldn't infinity over 1 = infinity, how is that any different then infinity, you fail to prove the difference between infinite and infinity. So now go back to some of the more ... repeated stuff. You at least do manage to say infinity itself is not a number, but seem to have an idea that infinite is a number in the first place. Pretty much using infinite to take the place of infinity. Though I can see potential uses for all this, why is this so important that you argue this? What you should do rather is find a way to prove it. It's interesting because I had just recently made a topic about discovering something new in math. If you are so heart set as to continue arguing this, why not at least find a way to prove it first, rather then continue this conflict which will likely get you nowhere?
There is quite a lot I disagree with here. First off, the very first sentence you say, unless I'm misunderstanding it, this yet again sounds like your own definition of it. The second sentence you say, not only do I not agree with that, but you also have a contradiction in there. Even based on things of what you've been saying, you used 0 in there, since you keep looking at it as fractions, I'm going to do the same: 0/infinity in YOUR definition does NOT equal 0? I don't feel like reexplaining the first part, because again, you seem to be going by your own definition there. Lastly, mathematically, based on current rules, that does not even make any sense. Throughout this whole post, whether or not you think infinity is a number, you continue to use it as one, demonstrating the difference as you say, "Mathematically." Yet doesn't this seem contradictory to your other idea of infinite? Either way, I have mostly made my argument; there are many ways to use infinity, wikipedia shows two such examples under real analysis...http://en.wikipedia.org/wiki/Infinity. I just hope you eventually begin to understand what infinity really is, so as to avoid all this confusion.
Remember when I said this...
You are proving my point exactly; you continue to argue this based on the way you see it and try to enforce it upon us without much proof besides for your own reasoning behind it. Yet you argue an already established idea and try to change the way things are, which I do not think you realize just how big of an impact that would also have. You take out the current idea and replace it with your own, what happens to everything that is dependent on the previous idea? Your new idea isn't a replacement for it, and if tried to, would present so many complications I don't even know where to begin. I just hope this helps a little... Life isn’t a simple Math: there are always other variables. [unknown] But Nature flies from the infinite, for the infinite is unending or imperfect, and Nature ever seeks an end. Aristotle #28 20121011 13:08:39
Re: Symbol for Infinitesimal?Hi again! Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional). LaTex is like painting on many strips of paper and then stacking them to see what picture they make. #29 20121011 13:15:40
Re: Symbol for Infinitesimal?I don't mind shaking things up a bit here. Last edited by ssybesma (20121011 14:01:21) #30 20121011 14:12:14
Re: Symbol for Infinitesimal?
I will. #31 20121011 16:30:08
Re: Symbol for Infinitesimal?
http://www.mathsisfun.com/numbers/infinity.html
That isn't quite right. Infinity is NOT an end to anything, regardless of how "impossible" you make it. It is just the opposite, endless. Infinity is not meant to be the final number to the number system, a number that every number equals, or a number being a fraction of infinity. Infinity just represents that it is endless. Let me give an example (incase you don't want to just look it up): If you are looking at 0.999... the nines go on forever, or infinitely. This is a correct way of using infinite.
Actually, you might be right about this. Back when I was working on it with my brother, he had me looking up a ton of stuff about it, and upon it I discovered that this was no longer an accepted usage of an infinitesimal, yet, trying to look it up now, I can see no evidence to this anymore. Now I didn't blindly look it up either back then, 1 over infinity I'd still argue from a mathematical standpoint still doesn't make sense. 1 IS a real number, yes, but you can NOT divide it by infinity (regardless of whether or not you are looking for an answer), because as I said earlier, infinity itself is not a number. The reason for this is because of what infinity is. Now, I actually can not find evidence that this no longer exists anymore, contrary to multiple posts I said earlier. Therefore, I can not argue you are actually wrong about that and I must apologize about that. I will continue to look this up farther to see if I can find evidence of this again...
Fair enough. I have no arguments for that in that case. Last edited by Calligar (20121011 16:37:03) Life isn’t a simple Math: there are always other variables. [unknown] But Nature flies from the infinite, for the infinite is unending or imperfect, and Nature ever seeks an end. Aristotle #32 20121013 18:28:17
Re: Symbol for Infinitesimal?Okay, so I would like to clear up something I did in fact have wrong. I've said numerous times stuff like this...
I would like to note that I was actually wrong about that. The problem and reason why I thought that was wrong was confusion when looking at definition of infinity. I am not misunderstanding infinity but rather what exactly others mean by 1/∞. See, I was looking at this number more mathematically, looking at what infinity is and one is, and thinking that you can not divide 1 by infinity. However, this more has to be seen from a different view. It does seem that it is acceptable to use this for an infinitesimal, because you break 1 up endlessly, thus giving you arguably the smallest possible number. Though, there is debate about this, it is not considered an officially wrong idea either. So, ssybesma, and to all others whom this might apply to, I would like to say I'm sorry for presenting any confusion about that... Last edited by Calligar (20121013 18:30:01) Life isn’t a simple Math: there are always other variables. [unknown] But Nature flies from the infinite, for the infinite is unending or imperfect, and Nature ever seeks an end. Aristotle #33 20121014 01:20:44
Re: Symbol for Infinitesimal?Well, if you want to have infinity and infinity in your number system it wouldn't be the integers. You would have to get a set Z*, change the axiom that says that there exists no biggest number and include infinity with the definition that it is greater than any number from the set Z and infinity with the definition that it is the number less than any number in Z. The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment 