0---------->(+n)+(-n) Cybermorphic, Let me direct you to another topic line where this process is discussed in greater detail. "Make it Finite if you can".
It seems a little like the sqrt(-1) situation.... but just because we can't find an answer hasn't stopped us from defining it as i or j and then using the whole concept in the real world to solve real problems. So it seems that just because something doesn't exist doesn't mean that it can't be useful - could the same apply here ? I imagine that all sorts of arguments could be laid down for proof of the non-existence of the quantity sqrt(-1) but there it is, like it or not.... imaginary it may be, but then again - what isn't ? What would happen if we just accepted (for a moment) that 1/0 is called # and it belongs to the set of....I dunno...how about 'fantasmagorical numbers'....... well now that it has a label and belongs to a family, can we make any use of it ? - like, can it help solve problems ? - isn't that the important bit ?
Good View Hilarion, I think you have a good view. But I find the topic more accademic than useful.Please Register or Log in to view the hidden image!
indeterminate forms are: 0/0 , inf/0 , 0/inf and inf/inf well maybe not o/inf I cant remember exactly when you say zero of them do you mean that there is zero zero's? without going into calculus, its a contradiction. if i have zero zero's dosn't that make it possible to be something since I don't have zero? in calculus its possible to turn an equation that ends up as 0/0 to inf/inf..... its indeterminate. we must change the form into one which is determinable. if you want me to explain this further I'm going to have to dig back into some notes.... as I can't pull it off the top of my head right now.Please Register or Log in to view the hidden image!
Frown ORW, Why the frown? You know this is fun.Please Register or Log in to view the hidden image! I like the view that "0" and Infinity are one and the same. Calculus tends to agree with that view but it seems to drive others crazy. Maybe that is why I like it.:m:
I'm only saying that as soon as you put zero in the numerator you've established how many of the items in the deminator there are. In terms of "order of operations" you don't have to perform any more if you have zero in the numerator, because you've already said there are zero of whatever is in the denominator. *shrug* I realize mathemeticians might argue, I'm just trying to make a practical point.
MacM: <i>I like the view that "0" and Infinity are one and the same.</i> You may like it, but it isn't true. <i>Calculus tends to agree with that view but it seems to drive others crazy.</i> Calculus does not agree with that view. wesmorris: <i>I'm only saying that as soon as you put zero in the numerator you've established how many of the items in the deminator there are.</i> No you haven't. If I have 8 ducks and I take them 2 at a time, how many groups of ducks do I have? Answer: 8/2 = 4. If I have no ducks and I take them 2 at a time, how many groups of ducks do I have? Answer: 0/2 = zero. If I have 8 ducks and I take them none at a time, how many groups of zero ducks do I have? Answer: 8/0 = infinity. I can have as many groups of zero ducks as I want. If I have no ducks and I take them none at a time, how many groups of ducks do I have? Answer: 0/0 = indeterminant. If I have no ducks to start with, can I really make groups from them? Maybe, maybe not.
Of course. You've got a valid point, but I'm just arguing that technically, you can't take zero ducks two at a time because you don't have any ducks to take because you just said you have zero of them. Of course. I was just saying that I disagree because of... I was taking the stance: "you can surely make te groups but the groups are only valueless placeholders until you put something there.. thusly.. you can think it... but it doesn't matter really. Thusly, zero over anything is just zero as I've previously stated. I'm not all that attached to it really, just thinking about it a bit and that's what I came up with.
Maybe it's indeterminant if you only think about it, but if you really want to DO it... then it's zero. *shrug* thoerizing.
Isn't dividing by zero the same as multiplying by it's reciprocal ? That means 0/1 = 0 * (1/0) = 0 If a Volkswagon is better than nothing And nothing is better than a Rolls Royce, Then does that mean that a Volkswagon is better than a Rolls Royce ? Seems as though 0 is the unmanifest form of number.......... x/0 = x/(-y) + x/(+y) indeterminable ? - yep, and then some, methinks. could zero be the mirror in which all other numbers are viewed ? If so, then we should be able to construct a "numerical laser" Please Register or Log in to view the hidden image! that utilizes bugger all at one end with near-enough to bugger all at the other end of a cavity that is pumped with random numbers. The result, I imagine, would be a highly collimated beam of intense nothingness.
How did that smiley face get there ?...... I was serious !Please Register or Log in to view the hidden image!
my apologies...... I meant 1/0 = 1/(-y) * 1/(+y) that should help..... and here was me tring to figure out why I was getting nothing but anti-nothingness out of this stupid laser! Well, it certainly explains why nothing seemed to be working right... whoooo....deja vu ! - I can clearly remember doing nothing like this before........must be my imagination.... it's probably nothing. don't worry, nothing I say means *anything*
1/(-y) * 1/(+y) = 1/-y^2 how do you know what the denominator is? 0/1=0/2=0/3.......what number do we choose? you cant say the denominator is 1 in this case, because other values will also work. also, look what happens if we flip the equation(which should still hold true for an equality) 1/0=2/0=3/0 if zero was a valid denominator, then 1=2=3 which we know is not true... the values are undefined in this case.
Re: Not well put In someway they r alike in the sense one is infinitely small (0) and the other one is infinitely large (infinity) - infiniteness is common. But in the case of 'infinitely small' we can apply the limit 0. In case of infinity we can't apply any limit. But we take both as sufficiently small / sufficiently large for the given purpose.
