Let's get into some second-order Cwelchian calculus to settle this once and for all, shall we?

First of all, let's define what 1 means. We use the Peano axioms, the foundation of all mathematics. It defines 1 as S(0), the natural number that immediately follows 0, the lowest natural number.

We also use the Peano definition of addition, which implies that

1 + 1 = S(1) = S(S(0)).

How, let's do a Taylor-Bergenstein analysis of this. We find that the function S(x) can be reticulated as

gamma_b(x) * (x -1 0 1 -x)^T dx

Of course, if we converge the recursive S(x) calls, we find through a binomial analysis that

(S(x)~~S(0)=>x) = gamma_b(x)^2 * theta_2(x + 0, 0) dx * (x -1 0 1 -x)^T dx * (0 -1 0 1 0)^T

Now, seeing as the second variable is a constant, we can use Curt's Theorem to simplify it:

(S(x)~~S(0)=>x) = gamma_b(x) + gamma_b(0) * theta_1(0, x) dx * (x 0 0 0 -x)^T dx * theta_0(0)

Now, as we have normalized the x decisive vector, we can do a theta substitution.

(S(x)~~S(0)=>x) = theta_1(x, 0) * (gamma_b(x) + gamma_b(0) * theta_0(x) dx)

See where this is heading? Now we evaluate the binomial constant:

theta_0(S(0)*S(0)) = gamma_b(0) + gamma_b(0) * theta_0(0)

We reverse the theta substitution and realize the recursive function call:

S(S(0)) = theta_1( (gamma_c(0, 0) * theta_0(0)) , 0)

And lastly, we create a Taylor series:

S(S(0)) = sum(i = 1 => inf) { 9 * 10^-i }

i.e.

S(S(0)) = 0.9 + 0.09 + 0.009 + 0.0009 + 0.00009 + ...

S(S(0)) = 0.9999999999999...

S(S(0)) = 1

...and since S(S(0)) means "that which follows that which follows 0", we find that

1 + 1 = 1

This, known as the Taylor-Newton paradox has been known since around the early 1700s. To this date, mathematicians haven't found the exact reason why that happens, but the common belief is that binomial analysis cannot be used with reticulated spatial data, although why that is has yet to be discovered as it works with any other number system. Others claim that theta substitution of constant coefficients causes an implicit division by zero, but that still doesn't explain why it works in non-spatial systems.

So yeah. Either something is fundamentally broken in mathematics or some of the smartest people in history weren't as smart as they thought they were.

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