SYSTEMS

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
                         
0.00000000000...2 etc.
                         0.11111111111...1 etc.
                         
0.99999999999...9

These 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 = 8

1 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.



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