Is there any reason, mathematicly, however, that undefined / undefined <> 1?AKG said:It's the latter. 1/0 is undefined, so it's certainly wrong that:
(meaningless symbol)/(meaningless symbol) = 1
Division is not defined for meaningless symbols, so there's no way to compute the quotient, let alone compute that it is 1.
I'm guessing you don't know what undefined means. Tell me, is a;kljdfa;lkjasdf greater than ;kljasdf;kljsdf? Does that previous question even make sense? No, it doesn't. x is a variable, and it's value is unknown or unspecified, not undefined. x stands for a number, and normally, we want to figure out what the number is by solving for x. 1/0 does not stand for any number. Division is an operation defined on numbers, so elephant/rhinoceros doesn't make sense. Similarly, (1/0)/(1/0) doesn't make sense, since 1/0 is not a number.eNathan said:Is there any reason, mathematicly, however, that undefined / undefined <> 1?
I mean 1/0 is undefined, but so is "x", but we all know x/x = 1 even though we dont know the value of x. Maybe my definition of "undefined" is wrong though :tongue:
If one were being carefull one would say something likeeNathan said:Is there any reason, mathematicly, however, that undefined / undefined <> 1?
I mean 1/0 is undefined, but so is "x", but we all know x/x = 1 even though we dont know the value of x. Maybe my definition of "undefined" is wrong though :tongue:
As AKG points out, [tex]\infty[/tex] is a mathematical concept; it is not a number, thus cannot be used as one in arithmetical operations.eNathan said:While we are on this strange topic, what about
inf / inf = 1
Therefore inf - inf = 0
eh?
how could this be done?GlauberTeacher said:And infinity could very well be defined over all the operations if we choose to define it that way.
yes, but that is also not true if you used any number (except 0).Jameson said:In other threads it has been pointed out that basic algebra cannot be applied to concepts such as infinity and divide by 0.
Is this true?
[tex]100\infty = 200\infty[/tex]
[tex]100 = 200*\frac{\infty}{\infty}[/tex]
[tex]100=200[/tex]
I think not.
It depends what is you want to do. For many purposes we wand to work with feilds. No feilds can be defined with zero division and infinite opererations. You could define a an extension so h^2=0 h not 0. Then we lose the zero product propert among other things (that is x*y can be zero without x or y being 0). Another approch is to define hyperreal numbers as is done in nonstandard analysis.quetzalcoatl9 said:how could this be done?
I presume things you mean things that behave like 1 ∞ = 2 ∞... because, for example, the hyperreals have lots of infinite numbers. (Meaning that they're larger in magnitude than any integer)No feilds can be defined with zero division and infinite opererations.
Yes that sentence of mine was a bit unclear. I did mean infinity in the sense of a number where x=2x=3x=x^2. Hyper reals avoid those type of difficulties by introducing and infinite number of infinite and infinitessimal numbers instead of one infinity. And the fact that even with hyperreals one still cannot divide by zero, but can divide by an infinite number of numbers that are like zero.Hurkyl said:I presume things you mean things that behave like 1 ∞ = 2 ∞... because, for example, the hyperreals have lots of infinite numbers. (Meaning that they're larger in magnitude than any integer)
I think you meant as "x" approaches infinity, not e.mathmike said:well here is proff that (1 / 0 ) / (1 / 0) = 0
take lim (x / e^x) as e approachs + inf.
lim (x / e^x) = lim [d/dx (x) ] / [d/dx (e^x)] = lim 1 / e^x = 0
eNathan said:Is there any reason, mathematicly, however, that undefined / undefined <> 1?
I mean 1/0 is undefined, but so is "x", but we all know x/x = 1 even though we dont know the value of x. Maybe my definition of "undefined" is wrong though :tongue: