Source of the post
Finally, if you insist that a scalar g divided by itself should itself (for g not equal to 1), then you quickly break math. Suppose g=7. Then if 7/7=7:
7 = 7^2
Source of the post
g isn't a variable but rather a completely separate number from the -1 and 1 plane
In this case g cannot equal 7, just as 1 cannot equal 7, the same math breaks down... g in this case is an entirely separate version of 1 and could be considered as g=1 but g+1 does not equal 2 but rather g+1 (complex). Other absurdities would be g^0=g, 2g*g=2g=2g^2, 2g/g=2g, it remains in its own plane, not a variable but as another 1. However I get what you are saying...
Source of the post
Consider the 3D Cartesian space with coordinates (x,y,z). The x, y, and z axes are each independent (mutually orthogonal). And together they span a three-dimensional space. Right? Now let's pick a point with coordinates (0,0,g). That's the point g units away from the origin along the +z axis. Then what do we get if we compute g/g?
In terms of scalars, g is the distance from the origin to the point (0,0,g). Then this distance divided by itself is 1. Always. "The number of times you must lay out a ruler of length g to reach a distance of g is equal to 1".
Source of the post
I think you're getting yourself confused over the behavior of numbers (scalars) vs. vectors. A number g divided by itself is never itself in any dimension except in the specific case that g=1. A vector g, divided by its length, is a new vector of length 1 in the direction of g.
So I see my fault is that imaginary numbers are a scalar measurement and not a vector, and that what I am doing is math as if numbers were a vector measurement. (0,0,g) divided by g if g was the vector-length (not length of vector) would indeed be g but the length itself would be 1. So this is actually extremely helpful! If I take the scalar math and multiply it by my vector math I should get the correct answer! I'll test it!... Success! The math is fixed! By using the vector quantity first when dealing with the transformations and then later multiplying it by the scalar, the imaginary numbers signs switch! Not only do they switch but they also lay on the same dimension instead of splitting into two other dimensions! The complex-real plane becomes the scalar (the line from the origin traced out to the vector in units of i). Everything checks out! So I guess we were both kinda right, except I was looking at vector minus scalar and you were looking at scalar and a real dependent vector. Multiplying the scalar independent vectors by the scalars after the math works! So it does suggest something though... Under the scalar independent vector system, imaginary numbers are not their own independent dimension but rather the scalar measurement between an independent dimension and another with its own scalar. So the "third" dimension of the sphere isn't imaginary, its the g vector, but the lines traced from the center to a vector can be imaginary, real, or complex. All the anomalies go away! I hope I got the right conclusion from this, all be it an obscure and strange one (like learning how to do math if the real plane had a third sign from -1 and 1)... And it is probably a strange rule I am using for this non-scalar math, where dimensions are given their own sets of 1s and -1s... But the math I used for it seems to be fixed now! Heres what I mean by the math being fixed: to transform from one side of my n-dimensional number sphere I use -n^-1, so lets go from -g to positive g where g is imaginary, we first use g instead of i treating g as an independent vector instead of a scalar (not converting to a scalar... which now that I think about it... is kind of a vector if it didn't have a scalar at all... or its own vector-scalar... weird) so we get -(-g)^-1, the inverse of -g in our weird plane where g/g=g, equals -g, then we do -(-g)... we get g... then we take g and multiply by i... and we get gi, which is indeed the opposite to -gi, and if we take out g... i and -i have successfully been transformed! If we just used i then we get this -(i)^-1, -(-i), i ... no sign switch. Now all I need to do is check some things and figure out what all of this means... I will leave some time before I edit my OP topic to reflect this... just in case I am terribly wrong... but hey! For being terribly wrong, I am getting terribly right answers!
Heres a picture of the correction, so you can see what I mean (instead of trying to understand my horrible grammar):
So ya... You were right! I was completely confusing vectors and scalars... but I wasn't completely wrong... A slight change in perspective and a slight modification to the math and everything works! So imaginary numbers are second dimensional but not independent vectors, they are a dependent scalar to a completely different independent second dimensional vector! By doing math on the second n-sphere above, imaginary numbers don't break down, math using them still works, and it makes some interesting predictions which I will have to study
LATER: Well... new problem... using i as the distance between the center and g works and all... but it changes a few things... it means what I am looking at isn't a unit sphere operating under normal rules... I could have suspected that by the fact that 0 and infinity falls on it... i and -i "lengths" change as the complex ratio between real numbers and "g" numbers change (as expected). But interesting things happen when i becomes 0*i... it is indeed completely in the real plane... but what does that mean? We get the right position but what is the "length"? Even more interesting is the possible implication that "length", "sphere", "vector", and "scalar" are all completely unrelated to this, that I am seeing something completely different and those are the closest words I can describe them with, but how they work do not correlate. "length" can change with angle, "vector" has no "scalar", the "sphere" is hyperbolic and only "looks" like a sphere and potentially has no bounds, "scalars" have hidden "vectors"... these are the wrong words but something is strange here... I am no longer investigating imaginary numbers at this point, they are safe in definition, rather... I am investigating something I don't know where it will take me and what it exactly means... I could be investigating something analogous to hyperbolic geometry, not "applicable" to Euclidean geometry but might be extremely applicable once figured out... I don't know... this is weird though... All because I wanted to see what would happen if I treated infinity as a number xD
To reality, through nothing, from un-everything.