ok I just got a kinda 'crazy' idea that would explain the arithmetic paradox.
if say, ∞/∞=A and 0/0=A;
pick 2 random numbers from A, just 2 and 3;
so
∞/∞=2
∞/∞=3
0/0=2
0/0=3
however 2\neq3;
∞/∞=2\neq3=∞/∞;
so ∞/∞\neq∞/∞, same goes for 0/0\neq0/0
so is it possible to say that:
∞\neq∞...
Is there an alternative symbol that can be used instead of '=', for a different logical expression? a=b means a and b are equivalent in quantity, however infinity and 0 are not ordinary quantities?
I can see that infinity does not 'equal' to infinity
(inf/inf=A)
but does 0 'equal' to 0???
(0/0=A)!
there are values other than 1 in A,
then is 0=0 false?
Trying to find a equation to explain it.
let there be y=0*x
there are 4 value ranges on the real plane:
I. x<0 y=inf
II. x=0 y=A
III. x>0 y=0
IV. x=inf y=A
as we can see here the value of y is like a sine wave;
(Although A is not a number.)
inf --> A --> 0 --> A --> inf --> A ....
so, does A represent a intermediate range of...
The red part is the wrong part.
By reverse you use e as a index for exponentiation, so lets say :
ln a = ln b - c
e^(ln a) = e^(ln b - c)
u got your exponentialtion wrong.
so if those things are true, then many of the limits can be viewed in a different perspective.
e.g.
lim->infinity (1+1/m)^m=e
u couldnt just substitute m=infinity into the equation;
however if we do that:
(1+0)^infinity=e
1^infinity=e
it makes sence now since e is a member of A.
thinking from the Riemann Sphere: can the real projective line be described as a circular graph?
So all the arithmetic calculations can be done via angular calculations, and 0 or infinity would have a unique angle from the axis?
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 [Broken]
Read these first before you criticise me...
x^3+bx=c
x(x^2+b)=c
x(x+ib)(x-ib)=c
ln (x(x+ib)(x-ib))=ln c
ln x + ln (x+ib) + ln (x-ib)=ln c
ln x + ln |x| + iarg(z) + ln |x| - iarg(z)=ln c
ln x + ln x + ln x = ln c
3ln x = ln c
ln x = (ln c)/3
x=e^(ln c)/3
if x^a=b (a,b are constants)
then there are two ways of finding x: root and log
so for example, x^2=4
by root:
(x^2)^(1/2)=(4)^(1/2)
x=\pm2
by log:
2 ln (x) = 2 ln 2
x=2
but it is yet impossible to obtain the negative x from logs. How are you supposed to do it? And heres a few...
Yes thank you Chiro. However I know this and this is not what I meant to find out.
What I am trying to do is to define the 'undefined' for things like 0/0 and ∞/∞ in the real projective plane.
I recall that 'undefined' A , and A has these properties:
A \bigcap R, and every number in R suits...
Is there a theory about one-sided "equations"?
I am working on infinity recently. Trying to define the 'indirect' result of infinity as 'range of numbers'. So its like: if there is a set A of infinite elements, f(x)=a\wedgeb\wedgec\wedged..... (a,b,c,d...\inA);
However, one cannot say a=f(x)...
I was trying to understand superlog and superroot but I get only 3/4 of them. Can anyone just explain, in a non-textbook way, such that:
I can understand without any post-calc knowledge
http://en.wikipedia.org/wiki/Superlog
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or just explain...
c = a^b = |a|^b x e^(ib) ?
so if a= -1, b=2 c=1; then |-1|^2*e^(2i) = e^2i?
i suppose that can only be e^2i∏ which equals to 1.
and whats this formula called?
Gelfond–Schneider theorem can be seen here(http://en.wikipedia.org/wiki/Gelfond%27s_theorem) wiki.
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Given a simple calculation:
a^b
where a<0;
and let b be a fraction : u/v
so there are 3 possible ways of u...
1 to the power of ∞ =e ?????
Let there be function f(x):
f(x)=(b+1)^(b+1)/(b+1!)/[(b^b)/b!]
--an example of f(99): 100^100/100!/(99^99/99!)
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and as b gets larger, f(x) converges to e.
so we have:
lim b→ ∞...