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• $\text{Blackboard Bold Symbols}:$

$\mathbb{N}:~\text{The set of natural numbers}$

$\mathbb{Z}:~\text{The set of integers}$

$\mathbb{Z}_n:~\text{The cyclic group modulo}~n$

$\mathbb{Q}:~\text{The set of rationals}$

$\mathbb{J}:~\text{The set of irrationals}~(\mathbb{Q}\cup\mathbb{J}=\mathbb{R})$

$\mathbb{R}:~\text{The set of real numbers}$

$\mathbb{R}^n:~\text{The}~n\text{th dimension real coordinate system}$

$\mathbb{C}:~\text{The set of complex numbers}~(\mathbb{R}\cap\mathbb{C}=\varnothing)$

$\mathbb{H}:~\text{The set of quaternions}$

$\mathbb{O}:~\text{The set of octonions}$

$\mathbb{D}_f:~\text{The domain of a function}~f$

• $\text{Toeplitz Conjecture}:$

$\text{Let}~J~\text{be the set of all Jordan curves and let}~j_k~\text{be an arbitrary element of}~J.\text{ Show that}$

$\text{there exists four points}~p_1,p_2,p_3,p_4~\text{on}~j_k~\text{such that}~p_1,p_2,p_3,p_4~\text{form the vertices of a}$

$\text{square}.$

$\text{Riemann Hypothesis}:$

$\text{Show that all non-trivial zeroes}~s~\text{of the Riemann zeta function}$

$\zeta(z)=\sum_{n=1}^{\infty}\frac{1}{n^z}$

$\text{satisfy}~\Re(s)=\frac{1}{2}$

$\text{Goldbach's Conjecture}:$

$\text{Show that, for all even natural numbers}~n~\text{there exists two primes}~p_1,p_2~\text{satisfying}$

$p_1+p_2=n$

$\text{Erdos - Strauss Conjecture}:$

$\text{Show that}~\exists{a,b,c}~\text{to the Diophantine equation}~\frac{4}{n}=\frac{1}{a}+\frac{1}{b}+\frac{1}{c}$

$\text{for all}~n\in\mathbb{N}$

• A Dream Within A Dream - Edgar Allen Poe

Take this kiss upon the brow!
And, in parting from you now,
Thus much let me avow-
You are not wrong, who deem
That my days have been a dream;
Yet if hope has flown away
In a night, or in a day,
In a vision, or in none,
Is it therefore the less gone?
All that we see or seem
Is but a dream within a dream.

I stand amid the roar
Of a surf-tormented shore,
And I hold within my hand
Grains of the golden sand-
How few! Yet how they creep
Through my fingers to the deep,
While I weep- while I weep!
O God! Can I not grasp
Them with a tighter clasp?
O God! Can I not save
One from the pitiless wave?
Is all that we see or seem
But a dream within a dream?

“A weapon based on Time . . ." mused Viktor Mulciber. "Well, why not? The one force no one knows how to defeat, resist, or reverse. It kills all forms of life sooner or later. With a Time-weapon you could become the most feared person in history."
"I'd rather be loved," said Root.
Mulciber shrugged. "You're young.”

- Thomas Pynchon, from Against the Day

“The rest of us, not chosen for enlightenment, left on the outside of Earth, at the mercy of a Gravity we have only begun to learn how to detect and measure, must go on blundering inside our front-brain faith in Kute Korrespondences, hoping that for each psi-synthetic taken from Earth's soul there is a molecule, secular, more or less ordinary and named, over here - kicking endlessly among the plastic trivia, finding in each Deeper Significance and trying to string them all together like terms of a power series hoping to zero in on the tremendous and secret Function whose name, like the permuted names of God, cannot be spoken... plastic saxophone reed sounds of unnatural timbre, shampoo bottle ego-image, Cracker Jack prize one-shot amusement, home appliance casing fairing for winds of cognition, baby bottles tranquilization, meat packages disguise of slaughter, dry-cleaning bags infant strangulation, garden hoses feeding endlessly the desert... but to bring them together, in their slick persistence and our preterition... to make sense out of, to find the meanest sharp sliver of truth in so much replication, so much waste...

- Thomas Pynchon, from Gravity's Rainbow

Heiligenstădter Testament - Ludwig van Beethoven

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