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leiyou
Member since Sep-3-02
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Sep-10-02, 06:13 AM (EST) |
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"a / 0 * 0 = a ?"
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does a / 0 * 0 = a? a ^ -b * a ^ b
=
a ^ (b - b)
=
1 then if a = 0 0 ^ -b * 0 ^ b = 1 that is true 1 / (0 ^ b) * 0 ^ b = 1 so, there are numbers a / 0 times by 0 and will give non 0 products? if so, isn't 0 ^ 2 = 0 ^ 1 = 0? then why 0 ^ - 1 * 0 ^ 2 = 0 ? if laws of indexes are applied? so does 0 ^ 2 = 0 ^ 1? and does 0 ^ -1 = 0 ^ - 2? also, if two pts on the y axis are (0,0) and (0,1) use the 2 pt formula, the equation of the y axis is as follows (y - 1) / (x - 0) = (1 - 0) / (0 - 0) and on the right hand side, the gradient is 1 / 0 and that is the gradient of the y axis i.e it's undef, but it can only be of one value so 1 / 0 = 2 / 0 = 3 / 0 ... then how can 1 / 0 * 0 = 1 and 2 / 0 * 0 = 2? also, (1 / 0) * 0 must equ to 1 if the equation of the y axis is to be derived (y - 1) / (x - 0) = (1 - 0) / (0 - 0) is (y - 1) / x = 1 / 0 let's think of the 0 as a times both side by a a ( y - 1) / x = 1 * a / a i.e a ( y - 1) = 1 * 1 * x but a = 0 so x = 0 why?????????????? can someone plz give some logical explanations? |
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Bo Jacoby
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Sep-10-02, 07:43 AM (EST) |
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2. "RE: a / 0 * 0 = a ?"
In response to message #0
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x=a/b means that x satisfies the equation bx=a .
Unless b=0, this equation has a unique solution.
Now, what if b=0 ?
x=a/0 says that x satisfies the equation 0x=a .
If a=0 , then any value of x will do.
Otherwise no value of x will do.
1/0 can mean no number.
0/0 can mean any number.
This is useless for computation.
So: don't divide by zero!
Trying to divide by zero leads to nonsense.
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Cino hilliard
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Oct-13-02, 06:54 PM (EST) |
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4. "RE: a / 0 * 0 = a ?"
In response to message #3
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>It's just that 0/0 and 0^0 cannot be defined in a way that
>works. When you fool around with these you end up with
>paradoxes like 1=2. 0^0 is defined as 1. This can be intuitively verified by
Limit (1/x)^0 as x -> inf = 1. Try (.0000001)^0 on your Sci Calculator. Unfortunately, the Hp 20s and Excel give error for 0^0. Most other languages basic, vbasic, c etc give 1. |
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alexb
Charter Member
862 posts |
Oct-13-02, 06:57 PM (EST) |
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5. "RE: a / 0 * 0 = a ?"
In response to message #4
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> 0^0 is defined as 1. Yes, sometimes. Far from always. > This can be intuitively verified by
> Limit (1/x)^0 as x -> inf = 1. Try (.0000001)^0 on your Sci
>Calculator. No need in a calculator to verify a0 = 1, for a > 0. |
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Cino hilliard
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Oct-20-02, 04:55 PM (EST) |
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7. "RE: a / 0 * 0 = a ?"
In response to message #6
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>NO 0^0 is not defined as one. It is an indeterminate form,
>like 0*infinity, infinity^0, 1^infinity, infinity/infinity
>and infinity -infinity. Not so. It is a matter of who is defining it. Indeterminate means it can be defined as 1.
0^0 is defined as 1 in maple, mathematica,vbasic, c,c++, numerous basics, hp 48g etc .
Excel had it as error
Here is a reasonable discussion on the subject. https://mathforum.org/dr.math/faq/faq.0.to.0.power.html
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Creon
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Oct-22-02, 10:28 AM (EST) |
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8. "RE: a / 0 * 0 = a ?"
In response to message #7
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Sorry but 0^0 will never be 1.
just put it in words, when you have nothing it can't become something.so the example as stated below is not correct because you can't compare .00000001 with 0  )
-----------------------------------------------
> This can be intuitively verified by
> Limit (1/x)^0 as x -> inf = 1. Try (.0000001)^0 on your Sci
>Calculator.
----------------------------------------------- Next statement is also very strange, since when is programmable software a link of what is correct in mathematics.
sure program's give an answer to the sum 0^0 because you have to disable the crash possibility of a computer so this is no reference.
If you want I can program the answer for you till the value 4000 but it won't still be correct ). -----------------------------------------------
0^0 is defined as 1 in maple, mathematica,vbasic, c,c++, numerous basics, hp 48g etc .
Excel had it as error
----------------------------------------------- |
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Michael
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Nov-04-02, 08:29 PM (EST) |
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9. "RE: a / 0 * 0 = a ?"
In response to message #8
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anything to the zero power is one, for the sake of things like numbering systems maybe i think, but zero to the zeroth power is zero, and i don't think that that is ambiguous or that there is any cause for fuss. |
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Lech
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Nov-05-02, 11:15 AM (EST) |
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10. "About 0^0"
In response to message #9
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The problem is that BOTH 0 and 1 should be correct values of 0^0:
0 because 0^x = 0 for any x, and
1 because x^0 = 1 for any x. And even more:
f(x) = (1/7)^(1/x) tends to 0, as x approaches 0.
g(x) = x tends to 0. But f(x)^g(x) tends to 1/7, as x approaches 0.
So I could claim that 0^0 = 1/7. I think it is better not to define 0^0 at all. Sometimes we suppose that 0^0 = 1 (for example), because it helps in calculation. But don't do it in general! |
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