# Search results

1. ### 1^∞, 0^0 and others on the real projective line

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∞...
2. ### 1^∞, 0^0 and others on the real projective line

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?
3. ### 1^∞, 0^0 and others on the real projective line

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.
4. ### 1^∞, 0^0 and others on the real projective line

But the problem for me is that I use computer in many different places, and I can't even read my own writing
5. ### 1^∞, 0^0 and others on the real projective line

I am so dumb. Used the hard way to do all the things. Because 1^inf=A then for any number n, n^inf=A because n^inf=n^inf * 1^inf =n^inf * A
6. ### 1^∞, 0^0 and others on the real projective line

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...
7. ### How do I write radian decimals in terms of Pi?

1.047/pi≈1/3 1/3*pi=pi/3
8. ### Laws of logs question

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.
9. ### 1^∞, 0^0 and others on the real projective line

This is very strange... ∞/0 =(n/0)/0 =n*(0^-2) =n/0 =∞ 0/∞ =(n/∞)/∞ =n*(∞^-2) =n*0 =0 And from that , ∞^∞=A and 0^∞=A
10. ### 1^∞, 0^0 and others on the real projective line

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.
11. ### 1^∞, 0^0 and others on the real projective line

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?

13. ### The best way to solve x³ + bx = c

now I look at my answer I got confused... cause the formula does not contain b so it is wrong???
14. ### The best way to solve x³ + bx = c

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
15. ### Simple question about logs

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...
16. ### The best way to solve x³ + bx = c

u mean 606087.936...? or 606087936
17. ### General mathematics problem on time taken to fill tank with pipes ,problem is below

Thats general algebra. Try to change the problem into values maybe helpful - thats what I do.
18. ### Is there a theory about one-sided equations ?

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...
19. ### Is there a theory about one-sided equations ?

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)...
20. ### Can someone just help explain a clear defination of superlog?

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 ------------------------------------------------- or just explain...
21. ### A counter-example to the Gelfond–Schneider theorem

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?
22. ### A counter-example to the Gelfond–Schneider theorem

Gelfond–Schneider theorem can be seen here(http://en.wikipedia.org/wiki/Gelfond%27s_theorem) wiki. ---------------------------------------------------------------------------------- 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...
23. ### 1 to the power of ∞ =e ?

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!) ------------------------------------------------------------------------- and as b gets larger, f(x) converges to e. so we have: lim b→ ∞...