ARRAY of Mathematics, using the Conservation Principle on proofs
Fundamental Theorem of Calculus
Statement of Fundamental Theorem of Calculus: The integral of calculus is the area under the function graph, and the derivative of calculus is the dy/dx of a point (x_1, y_1) to the next successor point (x_2, y_2). The integral is area of the rectangle involved with (x_1, y_1) and (x_2, y_2), and the derivative is the dy/dx of y_2 - y_1 / x_2 - x_1. Prove that the integral and derivative are inverses of one another, meaning that given one, you can get the other, they are reversible.
Proof of FTC::
You can always go from a trapezoid with slanted roof to being a rectangle, by merely a midpoint that etches out a right triangle tip which when folded down becomes a rectangle.
Here we see that a geometry diagram is ample proof of Fundamental Theorem of Calculus. And a geometry diagram is preferred for its simplicity and brevity, as the Pythagorean theorem started to do with mathematics in Ancient times. Other pieces and parts of the proof are scattered among the 10^60 facts and data of the Array of math. Here we show that a Statement is proven by a kernel of math knowledge-- you take a rectangle and procure a right triangle from the midpoint of the width and form a trapezoid for derivative and then reform back to a rectangle for integral. The derivative and integral pivot back and forth on a hinge at the midpoint of the rectangle width. The two operatives of integration and differentiation are reversible operators.
Fundamental Theorem of Algebra
Old Math statement of FTA:: The fundamental theorem of algebra states that every non-constant single-variable polynomial with complex coefficients has at least one complex root. This includes polynomials with real coefficients, since every real number A is a complex number with an imaginary part equal to zero.
Comment:: New Math statement theorem of FTA need not be so long, because in New Math we recognize that sqrt-1 is simply A/0 where A is a real-number (New Real Number).
Theorem-Statement of FTA:: given any polynomial with New Real Numbers, that there always exists at least one New Real Number, call it A, as a solution.
Proof of FTA: x^2 +1 = 0, goes to 1/x^2 = -1, with solution x=0 as 1/0 = sqrt-1, thus any polynomial is 1/polynomial = +-k has at least, one solution for A.
Comment:: Notice the beauty of the Statement of Theorem then Proof are almost identical in length of words. This is what happens when you have a true proof of a statement in mathematics.
Comment:: there is a huge fallout of this proof, in the fact that "i" an imaginary number is no longer needed because the Reals in 0 and any Real A where we have A/0 is a imaginary number and is a complex number. So, all of a sudden the Complex Plane and imaginary number dissolves out of math history into a gutter of shame. Whenever see "i" what that really is, is A/0 where A is any Real number.
Comment:: now the order of the ARRAY is desirable to be of a history order. But, in many cases, we can lump and repeat statements. Remember, the ARRAY is going to be huge. I am talking of volumes that would fill a entire library, just on math ARRAY. And of course, in our computer age, we have the ARRAY accessible by computer.
No point in reading or studying anything from Godel (Goedel). He was so stupid in Logic, that it escaped his attention that the AND connector is the add, and not the OR connector. Spending a whole life in Logic, yet Godel was so dumb in logic that he believed all his life that AND truth table was TFFF, when in reality it was TTTF. The only time a AND connector is false is when there is no true statement available at all. When everything is false, is the time that AND is false. And here we have a klutz of logic, spending his entire life in Logic and never smart enough to realize AND is the ADD of Logic, not OR.
Godel was so stupid in Logic, that OR is the choice connector, chose between A or B and thus Subtraction, not addition. The OR truth table is actually FTTF since it is true only when a "choice is available".
Yet this crippled mind of Godel is touted as some brilliant person because of his silly daft ideas of completeness and consistency. His fake proofs all hinge on the notion that Infinity is poorly defined. Infinity has no borders. But if you realize that Infinity has a borderline, you cannot use infinity to pull your stupid fake proof along. So, just as Godel was ignorant of not knowing AND was Add, equally, he was ignorant that he misused the concept of infinity to make fake proofs.
So Godel is a man that was too dumb to realize AND was Add and not OR, and then, why would any rational person think that such a failure of Logic has anything to say about math completeness or consistency. He could not even tell the difference between add and subtract.
I should put this as a Comment in the ARRAY.
Now, one aspect of Godel that should have alerted people that he was bad in thinking, is that he kept thinking people were trying to poison him. And so he decided on starving to death, rather than eat some food he was deluded into thinking it was poison. Now, do you think a person of that type of mind can find truths of Nature of a complex form? No, a person who lives a life of crazy reason, only has crazy ideas to offer.
Comment:: Only during the time of Archimedes Plutonium, do mathematicians begin to look at the personal character of mathematicians and of physicists, to ponder, if living a crazy life, means, that the science work offered by such a person-- is also, just plain crazy.
Very crude dot picture of 5f6, 94TH
ELECTRON DOT CLOUD of 231Pu
::\ ::|:: /::
::/ ::|:: \::
One of those dots is the Milky Way galaxy. And each dot represents another galaxy.
. \ . . | . /.
. . \. . .|. . /. .
--------------- (Y) -------------
. . /. . .|. . \. .
. / . . | . \ .
whole entire Universe is just one big atom
where dots of the electron-dot-cloud are galaxies
I re-opened the old newsgroup PAU of 1990s and there one can read my recent posts without the hassle of spammers, off-topic-misfits, front-page-hogs, stalking mockers, suppression-bullies, and demonizers.