25 Jul 06
Originally posted by Ramiri15Ok I read the article in wikipedia and it just states the same tired arguments which boil down to essentially..."we have to state O!=1 or else it screws up a bunch of our number theories"
Search "empty product" on Wikipedia for a nice explanation. By the way, in response to Bowmann, infinity - infinity is an indeterminate form, therefore the operation can't be performed.
Just because something screws up a model that works well for most things, it doesn't mean you should discount it, or fix it by just making a statement that is more philosophical than it is mathematics..(0 ways= 1 way)
That would be like all those early String Theory scientists saying, " oh those anomolies? uh, ya, just ignore that, our model works better if you ignore those anomolies" Instead, they went back and fixed their model.
Perhaps a re-visit of this 0=1 nonsense would prove uzfull
25 Jul 06
Originally posted by uzlessIt's not 0=1, you're getting it wrong.
Ok I read the article in wikipedia and it just states the same tired arguments which boil down to essentially..."we have to state O!=1 or else it screws up a bunch of our number theories"
Just because something screws up a model that works well for most things, it doesn't mean you should discount it, or fix it by just making a statement that is more philos ...[text shortened]... back and fixed their model.
Perhaps a re-visit of this 0=1 nonsense would prove uzfull
An empty product needs to be 1 to be coherent with all the other properties of products.
x^0=1 is again an empty product being equal to 1. Here it is easy to verify by the properties of exponentials that unless it is so a lot of inconsistencies would arise. You can also verify by tracing the function a^x that the limit when x->0 must be 1 to ensure the continuity of the function.
Don't forget that all Mathematics ultimately rest on axioms (regarding its operations, for example). If these axioms were not consistent, then the usefulness of mathematics as a tool would be greatly reduced.
25 Jul 06
Originally posted by uzlessas mr delivery said, there is only one way of arranging 0 giraffes on his kitchen table-the way where there is none. thus, 0!=1...
Ok I read the article in wikipedia and it just states the same tired arguments which boil down to essentially..."we have to state O!=1 or else it screws up a bunch of our number theories"
Just because something screws up a model that works well for most things, it doesn't mean you should discount it, or fix it by just making a statement that is more philos ...[text shortened]... back and fixed their model.
Perhaps a re-visit of this 0=1 nonsense would prove uzfull
25 Jul 06
Originally posted by GinRoseThe reason that the reasons given so far seem unnatural to some posters is because they don't properly understand that mathematics is currently founded upon functions mapping sets to sets - rather than formulae containing numbers and letters.
OK now tell me why 1!=1, but 0! also =1. I just never got it.
26 Jul 06
Originally posted by uzlessYou really are useless.
Ok I read the article in wikipedia and it just states the same tired arguments which boil down to essentially..."we have to state O!=1 or else it screws up a bunch of our number theories"
Just because something screws up a model that works well for most things, it doesn't mean you should discount it, or fix it by just making a statement that is more philos ...[text shortened]... back and fixed their model.
Perhaps a re-visit of this 0=1 nonsense would prove uzfull
26 Jul 06
2 edits
Originally posted by TommyCIgnoring Xanthos's trailer park comment for the moment, you are referring exactly to what I am getting at. My question is not necessarily whether or not 0!=1 is correct, but rather whether or not a mathematical system that we have devised requiring 0!=1 to be correct is a system we should be using in the first place.
The reason that the reasons given so far seem unnatural to some posters is because they don't properly understand that mathematics is currently founded upon functions mapping sets to sets - rather than formulae containing numbers and letters.
You state mathematics is currently founded upon functions mapping sets to sets. Is there an alternative foundation upon which we can draw upon that would not require 1!=1 and 0!=1 at the same time?
This may require some thought, but then again, I've noticed most posters here don't like to stray outside of their own presumptions and usually respond with some derogative derivitive of their own intransagence....even if this is a "Posers and Puzzles" board!
Edit: As Palynka said, "An empty product needs to be 1 to be coherent with all the other properties of products"
The fact that an empty product NEEDS to be 1 to be coherent with all other properties of products raises a red flag...Einstein created the Cosmological Constant because he NEEDED it to fit his model of the Universe...turns out it was just his model that was wrong.
26 Jul 06
1 edit
I don't think any professional mathematicians spend any time worrying why 0!=1. It is *defined* that way, (motivation for definition: convenience). End of story. It doesn't matter *why*, strictly speaking, it is a *definition*. You could equally well define it to be 258732057, but that would be very silly.
The reasons why 0!=1 happens to be convenient are given above. There are at least three good ones I've seen.
Mathematics is not about these kinds of issues. It is much more intricate and substantial.
26 Jul 06
1 edit
Originally posted by SPMarsAgain, just because it's convenient to define something, it doesn't necessarily make it right.
I don't think any professional mathematicians spend any time worrying why 0!=1. It is *defined* that way, (motivation for definition: convenience). End of story. It doesn't matter *why*, strictly speaking, it is a *definition*. You could equally well define it to be 258732057, but that would be very silly.
The reasons why 0!=1 happens to be convenient
Mathematics is not about these kinds of issues. It is much more intricate and substantial.
You say it doesn't matter *why* because it's a *definition*...why do you take this definition on face value? Just because we are taught it's a definition and therefore irrefutable?
Is it possible this definition is wrong? Is there a way to test this definition? Or do we simply go along with it and accept it blindly?
Most of our "problems" in math come from the use of zero. To get around this "problem" we either define it (as in 0!=1) or we say it is "undefined" (5/0=?).
Is it okay to just say that our current system of mathematics doesn't handle zero all that well, or do we take a closer look. If you are comfortable with the notion of just defining things for convenience as long as the end solution is correct, then the current system is perfect for you and will yield reliable repeatable and correct answers. I just wonder if there is another way built on different axioms than our current number system. Kind of like QWERTY keyboards vs Dvorak. 😉
26 Jul 06
Originally posted by uzlessYou remind me of someone I used to call "The Master Of The Empty Set".
Again, just because it's convenient to define something, it doesn't necessarily make it right.
You say it doesn't matter *why* because it's a *definition*...why do you take this definition on face value? Just because we are taught it's a definition and therefore irrefutable?
Is it possible this definition is wrong? Is there a way to test this definiti ...[text shortened]... axioms than our current number system. Kind of like QWERTY keyboards vs Dvorak. 😉
😉
26 Jul 06
3 edits
Originally posted by SPMars
You remind me of someone I used to call "The Master Of The Empty Set".
😉
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Er...no, as you can see on the left, that is definitely me.
Hey uzless, what about 0^0?
26 Jul 06
Originally posted by ThudanBlunder0^0
Originally posted by SPMars
[b]You remind me of someone I used to call "The Master Of The Empty Set".
😉
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Er...no, as you can see on the left, that is definitely me.
Hey uzless, what about 0^0?[/b]
That looks an awful lot like the face of those video game robots on "Berzerk" that used to chase you around the screen...."Get the Humanoid!"