04/26/2008, 05:06 PM
GFR Wrote:@Ivars: In other words, we should also have (if these operations ... exist):
2[-1]2 = 4 (minusation) !! and
2[w]2 = 4 (omegation) where w (omega .. !) is the first infinite, coutable, ordinal number.
The hypothetical cases of 2[ i]2 = 4, as well as of 2[0.5]2 = 2[1.5] = 2[2.5]2 = 4, should be supported by more serious considerations. However, ... why not??!! We shall see.
GFR
Do I really have to read about those ordinals? They sound scary.With what purpose? I think numbers have fine structure, is it explained by these ordinals?
What about i [ i] i ? Value and meaning? Related to :
0[0]0
1[1]1
2[2]2
3[3]3
4[4]4
x[x]x
i[ i]i
z[z]z
q[q]q where q is quaternion...
I think I know what is "imagination" . It is , even if I know you will say it can not be , related to ordering/enumeration in time. As opposed and complementing to ordering in space, or dimension(s) represented by real hyperoperations.
I have to think what then it means when applied to various bases and simple cases.
Ivars