- #1
n_kelthuzad
- 26
- 0
http://en.wikipedia.org/wiki/Real_projective_line
https://www.physicsforums.com/showthread.php?t=591892
https://www.physicsforums.com/showthread.php?t=592694
https://www.physicsforums.com/showthread.php?t=530207
Read these first before you criticize me.
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Working on infinity and the progress is very very slow. (maybe mainly because I am so lazy)
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under the conditions that 1/0=∞, 1/∞=0 and so on;
I assumed that 0*∞, ∞/∞ and 0/0 share the same answer;
thats answer is, not a number but a 'collection' of numbers(not a set with defined ranges yet)
I call that answer A
all the real numbers are assigned to A, in most conditions I can say it is true;
and let's go to the practical things.
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take any number from A: let's just call it n,
n^0=1
substitute 0=n/∞
n^(1/∞)=1
however if we apply basic exponentiation rule that:
x^y=z if and only if x=z^(1/y)
so n=1^(1/(1/∞))
n=1^(∞)
so that is, 1^∞=A
(in fact from this it can be also proven that for any nonzero real number n, n^∞=A;But I couldn't find that piece of paper.)
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0^0
it is true that 0=-n+n and (x^y)*(x^z)=x^(y+z)
so 0^0=0^1*0^(-1)
0^0=0*(1/0)
0^0=0*∞
or 0^0=(1/∞)*∞
=∞/∞
0^0=A
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∞^0
=(n/0)^0
=(n^0)/(0^0)
=1/A
=A
----------------------------------------------------------------------
for ∞^∞ and 0^∞; they are being worked on but in fact that (∞^∞)*(0^∞)=A
----------------------------------------------------------------------
so that's all the practical usage of A that I've worked out for now. However the definition of A is still unclear and needs a lot of work. Hope anyone can give me some pointers.
Victor Lu,
16
BHS, CHCH, NZ
https://www.physicsforums.com/showthread.php?t=591892
https://www.physicsforums.com/showthread.php?t=592694
https://www.physicsforums.com/showthread.php?t=530207
Read these first before you criticize me.
----------------------------------------------------------------------
Working on infinity and the progress is very very slow. (maybe mainly because I am so lazy)
----------------------------------------------------------------------
under the conditions that 1/0=∞, 1/∞=0 and so on;
I assumed that 0*∞, ∞/∞ and 0/0 share the same answer;
thats answer is, not a number but a 'collection' of numbers(not a set with defined ranges yet)
I call that answer A
all the real numbers are assigned to A, in most conditions I can say it is true;
and let's go to the practical things.
----------------------------------------------------------------------
take any number from A: let's just call it n,
n^0=1
substitute 0=n/∞
n^(1/∞)=1
however if we apply basic exponentiation rule that:
x^y=z if and only if x=z^(1/y)
so n=1^(1/(1/∞))
n=1^(∞)
so that is, 1^∞=A
(in fact from this it can be also proven that for any nonzero real number n, n^∞=A;But I couldn't find that piece of paper.)
----------------------------------------------------------------------
0^0
it is true that 0=-n+n and (x^y)*(x^z)=x^(y+z)
so 0^0=0^1*0^(-1)
0^0=0*(1/0)
0^0=0*∞
or 0^0=(1/∞)*∞
=∞/∞
0^0=A
----------------------------------------------------------------------
∞^0
=(n/0)^0
=(n^0)/(0^0)
=1/A
=A
----------------------------------------------------------------------
for ∞^∞ and 0^∞; they are being worked on but in fact that (∞^∞)*(0^∞)=A
----------------------------------------------------------------------
so that's all the practical usage of A that I've worked out for now. However the definition of A is still unclear and needs a lot of work. Hope anyone can give me some pointers.
Victor Lu,
16
BHS, CHCH, NZ
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