ThatWattPadGUY420

These stories will be continued on HinnyyForLife since I forgot this accounts password.

Also start at the BOTTOM.

If you want more confusing proof got to
          https://en.wikipedia.org/wiki/Proof_of_impossibility

Three famous questions of Greek geometry were how:
          
          ... with compass and straight-edge to trisect any angle,
          to construct a cube with a volume twice the volume of a given cube
          to construct a square equal in area to that of a given circle.
          For more than 2,000 years unsuccessful attempts were made to solve these problems; at last, in the 19th century it was proved that the desired constructions are logically impossible.[9]
          
          A fourth problem of the ancient Greeks was to construct an equilateral polygon with a specified number n of sides, beyond the basic cases n = 3, 4, 5 that they knew how to construct.
          
          All of these are problems in Euclidean construction, and Euclidean constructions can be done only if they involve only Euclidean numbers (by definition of the latter) (Hardy and Wright p. 159). Irrational numbers can be Euclidean. A good example is the irrational number the square root of 2. It is simply the length of the hypotenuse of a right triangle with legs both one unit in length, and it can be constructed with straightedge and compass. But it was proved centuries after Euclid that Euclidean numbers cannot involve any operations other than addition, subtraction, multiplication, division, and the extraction of square roots.
          
          Angle trisection and doubling the cube
          Both trisecting the general angle and doubling the cube require taking cube roots, which are not constructible numbers by compass and straightedge.
          
          Squaring the circle
          {\displaystyle \pi }\pi  is not a Euclidean number ... and therefore it is impossible to construct, by Euclidean methods a length equal to the circumference of a circle of unit diameter[10]

The proof by Pythagoras (or more likely one of his students) about 500 BCE has had a profound effect on mathematics. It shows that the square root of 2 cannot be expressed as the ratio of two integers (counting numbers). The proof bifurcated "the numbers" into two non-overlapping collections—the rational numbers and the irrational numbers. This bifurcation was used by Cantor in his diagonal method, which in turn was used by Turing in his proof that the Entscheidungsproblem, the decision problem of Hilbert, is undecidable.
          
          It is unknown when, or by whom, the "theorem of Pythagoras" was discovered. The discovery can hardly have been made by Pythagoras himself, but it was certainly made in his school. Pythagoras lived about 570–490 BCE. Democritus, born about 470 BCE, wrote on irrational lines and solids ...
          
          — Heath,[citation needed]
          Proofs followed for various square roots of the primes up to 17.
          
          There is a famous passage in Plato's Theaetetus in which it is stated that Teodorus (Plato's teacher) proved the irrationality of
          
          {\displaystyle {\sqrt {3}},{\sqrt {5}},...,}\sqrt{3}, \sqrt{5}, ...,
          taking all the separate cases up to the root of 17 square feet ... .[7]
          
          A more general proof now exists that:
          
          The mth root of an integer N is irrational, unless N is the mth power of an integer n".[8]
          That is, it is impossible to express the mth root of an integer N as the ratio ​a⁄b of two integers a and b, that share no common prime factor except in cases in which b = 1.

The obvious way to disprove an impossibility conjecture by providing a single counterexample. For example, Euler proposed that at least n different nth powers were necessary to sum to yet another nth power. The conjecture was disproved in 1966, with a counterexample involving a count of only four different 5th powers summing to another fifth power:
          
          275 + 845 + 1105 + 1335 = 1445.
          A proof by counterexample is a constructive proof, in that an object disproving the claim is exhibited. In contrast, a non-constructive proof of an impossibility claim would proceed by showing it is logically contradictory for all possible counterexamples to be invalid: At least one of the items on a list of possible counterexamples must actually be a valid counterexample to the impossibility conjecture. For example, a conjecture that it is impossible for an irrational power raised to an irrational power to be rational was disproved, by showing that one of two possible counterexamples must be a valid counterexample, without showing which one it is.

Proof by contradiction
          One widely used type of impossibility proof is proof by contradiction. In this type of proof, it is shown that if something, such as a solution to a particular class of equations, were possible, then two mutually contradictory things would be true, such as a number being both even and odd. The contradiction implies that the original premise is impossible.
          
          Proof by descent
          Main article: Proof by infinite descent
          One type of proof by contradiction is proof by descent, which proceeds first by assuming that something is possible, such as a positive integer[6] solution to a class of equations, and that therefore there must be a smallest solution. From the alleged smallest solution, it is then shown that a smaller solution can be found, contradicting the premise that the former solution was the smallest one possible—thereby showing that the original premise (that a solution exists) must be false.There are two alternative methods of disproving a conjecture that something is impossible: by counterexample (constructive proof) and by logical contradiction (non-constructive proof).

A problem arising in the 16th century was that of creating a general formula using radicals expressing the solution of any polynomial equation of fixed degree k, where k ≥ 5. In the 1820s, the Abel–Ruffini theorem (also known as Abel's impossibility theorem) showed this to be impossible,[4] using concepts such as solvable groups from Galois theory—a new subfield of abstract algebra.
          
          Among the most important proofs of impossibility of the 20th century were those related to undecidability, which showed that there are problems that cannot be solved in general by any algorithm at all, with the most famous one being the halting problem. Other similarly-related findings are those of the Gödel's incompleteness theorems, which uncovers some fundamental limitations in the provability of formal systems.[5]
          
          In computational complexity theory, techniques like relativization (see oracle machine) provide "weak" proofs of impossibility excluding certain proof techniques. Other techniques, such as proofs of completeness for a complexity class, provide evidence for the difficulty of problems, by showing them to be just as hard to solve as other known problems that have proved intractable.

A proof of impossibility, also known as negative proof, proof of an impossibility theorem, or negative result, is a proof demonstrating that a particular problem cannot be solved as described in the claim, or that a particular set of problems cannot be solved in general.[1] Proofs of impossibility often put decades or centuries of work attempting to find a solution to rest. To prove that something is impossible is usually much harder than the opposite task; as it is often necessary to develop a theory.[2] Impossibility theorems are usually expressible as negative existential propositions, or universal propositions in logic (see universal quantification for more).
          
          Perhaps one of the oldest proofs of impossibility is that of the irrationality of square root of 2, which shows that it is impossible to express the square root of 2 as a ratio of integers. Another famous proof of impossibility was the 1882 proof of Ferdinand von Lindemann, showing that the ancient problem of squaring the circle cannot be solved,[3] because the number π is transcendental (i.e., non-algebraic) and only a subset of the algebraic numbers can be constructed by compass and straightedge. Two other classical problems—trisecting the general angle and doubling the cube—were also proved impossible in the 19th century.

Weird thought, but:
          It's possible for nothing to be possible, because impossible has impossible in it, so possible isn't real, so if possible is impossible, then what has the human race really done on this Earth?
          Confused?
          Hold on, I got this from wikipeadia.