SYSTEMS0.00000000000...2 etc.MATHEMATICS Decimal System 1 . = one 2 .. = two 3 ... = three 4 . . . . = four 5 . . . . . = five 6 . . . . . . = six 7 . . . . . . . = seven 8 . . . . . . . . = eight 9 . . . . . . . . . = nine 10 = 9 + 1 = ten 20 = 10 + 10 = twenty 30 = 20 + 10 = thirty 40 = 20 + 20 = forty 50 = 30 + 20 = fifty 60 = 40 + 20 = sixty 70 = 50 + 20 = seventy 80 = 40 + 40 = eighty 90 = 50 + 40 = ninety 100 = one hundred (90 + 10) 200 = two hundred (100 + 100) 1000 = one thousand (500 + 500) 1,000,000 = one million (1000 * 1000) Infinitesimal numbers = 0.00000000000...1 0.11111111111...1 etc.0.99999999999...9These are small, infinitely repeating numbers.Rational numbers. These are numbers with values expressible in fractions and mathematical relationships. X = any number. Y = any number, possibly different from X. Z= any number, possibly different from X and Y 10X = 10 of any number. X / Y = Any number divided by any number. 3X / Y = Any number divided by any number in which 3X tends to be three times larger than Y.Equations 1 + 1 = 2 2 + 3 = 5 2 * 10 = 20 1 / 10 = 0.1 1/100 = 0.01 1/1000 = 0.001 10 / 20 = 1/2 = 0.5 10X = Y = Y is exactly 10 * X That is the same as writing 10X - Y = 0. Squares and Square Roots 0 ^ 1 = 0 * 1 = 0 1 ^ 0 = 1 * 1 = 1 2 ^ 0 = 1 * 1 * 1 = 1 etc. 1 ^ 2 = 1 * 1 = 1 1 ^ 3 = 1 * 1 * 1 = 1 2 ^ 2 = 2 * 2 = 4 2 ^ 3 = 2 * 2 (= 4) * 2 = 81 root of any number is that number. The 2 root of any number is the square root of that number. The square root of 4 is 2, because two 2s multiply to equal 4. Number Sq. Rt. ----------------------------- 4 2 9 3 16 4 25 5 36 6 49 7 64 8 Scientific Notation 1 X 10 ^1 = 10 1 X 10 ^2 = 100 1 X 10 ^ 3 = 1000 1 X 10 ^ 4 = 10,000 1 X 10 ^ 5 = 100,000 1 X 10 ^ 6 = 1,000,000 etc. Trans-Finite Numbers 1/ 0 = Infinity 2/ 0 = 2 * Infinity = Infinity Infinity * Infinity = Infinity Infinity / 2 = Infinity Differential Calculus (Part I.) Calculus is stupid. Calculus is for extroverts. It’s either totally easy, or you learn calculus. Calculus is about thinking —-wait that’s for philosophers. The origin is a variable. The derivative is the angle of a line —- that’s a small thing somehow, however, isn’t it? The process might be unlimited. Even the opposite mathematics has its limits. It also may have no function. There are no opposites in calculus: there are only functions. Structures are imaginary. Applied calculus is the tough part—for which you have your handy calculator. You can’t be on the side of calculus—- Calculus just IS. One thing to know is that calculus always has a power. If you input zero you get zero, just like in algebra. Advanced concepts in calculus: 1. Everything of value is outside calculus. 2. Maybe +3. 3. Calculus for all integers. That’s just an idea. It’s arbitrary in God’s logic is one of the first things I learned. Even now in calculus there is a division between professors who teach calculus as intuition and those that teach it as pure mathematics. Ultimately there may be more than one way to do calculus but remember, calculus is stupid , or you’re a genius. Towards the end of his life, Leibniz lamented: what’s human about calculus? So, calculus does have a downside. I’ll leave that as a puzzle. Integral Calculus (Part II.) Wrong! Doubly wrong! Specifics don't matter. Form a hypothesis, then throw it away! Apply the existing hypothesis, be conventional. Get it right! It concerns science! Be scientific! Clouds are clocks! Simplify always! Stay distanced from your work. Or pull an Einstein. Know. Philosophy is contraband. The rest is history. Posterior Calculus (Part III.) Now, I told you it wasn't about philosophy, but it is! All you need to know at first is Delta V. Whatever you interpret from is analytic a posteriori. Because you know you will get what results—- You have to begin somewhere, so you begin with the effect of an unseen cause. The cause is analytic. Delta V. is when you attach an effect to a cause—-And you call it —- what do you call it? Analytic. The rest is logic… I’m sure you can figure it out. It depends on the case. Concluding Remarks Sometimes we think calculus is a disease. Sometimes we think it is not logical at all. But mostly we think it is a highly useful thinking tool. Perhaps you’ll side with the Leibniz who thought it was inhuman, or perhaps you’ll side with the Leibniz who brought it upon himself to invent calculus. See Also: Advanced Calculus.BACK TO SYSTEMS |