Is there objective Truth?

[Aractus]

Just because we gave a name to describe what we observe in the natural world, doesn't mean we invented the observation. The golden rule exists wether or not we are here to observe it.

We didn't give a name to something we observed, Mathematics is invented. It's wholly artificial.

What about complex numbers (described using so-called "imaginary numbers")?

√(-1) = i
i2 = -1

A complex number is a number in the form of x = a +bi

You can expand from there into the quaternion numbers:

i2 = j2 = k2 = ijk = -1
ij = -ji = k
ji = -ij = -k
jk = -kj = i
kj = -jk = -i
ki = -ik = j
ik = -ki = -j

A quaternion number is a number in the form of x = a + bi + cj + dk

From there you can go to the octonions (used in String Theory).

An octonion number is a number in the form of "x= a + bi + cj +... + ho", although that's not how they're written they're written thusly:

x = x0e0 + x1e1 + x2e2 + x3e3 + x4e4 + x5e5 + x6e6 + x7e7

From there you could move on to the sedenions (/hexadecanion numbers), and probably not of much use in anything at all:

x = x0e0 + x1e1 + x2e2 + x3e3 + x4e4 + x5e5 + x6e6 + x7e7 + x8e8 + x9e9 + x10e10 + x11e11 + x12e12 + x13e13 + x14e14 + x15e15

And you can keep on expanding your dimensional plane as far as you wish to go. Don't forget you have to come up with all the other increasing complicated rules for calculating hypercomplex numbers in ways other than straight addition as well. An interesting property of sedenions is they contain zero divisors - that is it is possible to construct an product where numbers in the equation are non-zero but divide to zero:

(xn1en1 + xn2en2)(xn3en3 + xn4en4) = 0

Where:
xn1en1 + xn2en2 ≠ 0
xn3en3 + xn4en4 ≠ 0

So what we apply in mathematics is constricted to what we need because it ultimately leads to nonsense like the above. Or equations that just cannot be solved anyway like 1/0 = ?