## Math Lesson 1: Addition

Do you think math is hard? Well, it's actually really easy! Let's learn about addition. Addition is easy, follow Ex. 1

Ex. 1:

411

+376

___

787

Did you see what we did? Well we added up the digits and got 787, wow!

Ex. 2:

8,927

+1,009

____

9,936

Wait, what? How is 2+0=3? Well, it's simple, it's because of carrying. Carrying is when the digit that is right 1 digit overflows, where there is not enough digits to use.

Ex. 2.1:

8,927

+1,009

____

9,920

16

____

9,926

It's time for you to practice!

Pr. 1:

16

+21

__

??

Pr. 2:

344

+519

___

???

Pr. 2.1:

344

+519

___

???

??

___

???

This is the end of the lesson, bye!

## Surreal Games and Numbers

As many who are into recreational mathematics may have heard
about, there is a certain class of numbers which defies all
intuition even among those who have worked with the likes of the
infinitesimals found in calculus or the transfinite ordinals and
cardinals contained within set-theory. These numbers are truly so
out of this world they have been called *surreals* for a
reason.

When researching surreal numbers however, a friend wished to
know how they are related to games of *Hackenbush*. Frankly
I've always more interested in trying to understand the technical
definition of surreals than with some stick-figure game, but
putting all hesitancy to the wayside, I will explain how both work
to form the marvelous class of numbers John Horton Conway ma…

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## Advanced mathematics

- This article is a continuation of Intermediate mathematics

- 1 Equivalence
relation
- 1.1 Modular arithmetic

- 2 See also
- 3 References

From Wikipedia:Equivalence relation:

An Equivalence relation is a generalization of the concept of "is equal to". It has the following properites:

*a*}} (reflexive property),- if
*b*}} then*a*}} (symmetric property), and - if
*b*}} and*c*}} then*c*}} (transitive property).

As a consequence of the reflexive, symmetric, and transitive properties, any equivalence relation provides a partition of the underlying set into disjoint equivalence classes. Two elements of the given set are equivalent to each other if and only if they belong to the same equivalence class.

Back to top

From Wikipedia:Modular arithmetic :

Modular arithmetic can be handled mathe…

## Elementary mathematics

- 1 Positive numbers
- 1.1 Addition

- 2 Further reading
- 3 References

- See

- Introductory mathematics

## Introductory mathematics

- This article is a continuation of Elementary mathematics

Believe it or not the basis of all of mathematics is nothing more than the simple function.

- Next(0)=1
- Next(1)=2
- Next(2)=3
- Next(3)=4

This defines the . Natural numbers are those used for counting.

- These have the very convenient property of being . That means that if a

## Proof that 1+2+3+4+5....... is NOT = -1/12

We can first start out by simplifying adding all previous numbers to the current number. If you want to solve 1+2+3+4..........+n, an equivalent way to solve this is, (n+1)(n/2). Examples: 1+2+3 = 4*1.5 = 6, and 3+2+1 = 6. 1+2+3+4 = 5*2 = 10, and 1+2+3+4 = 10.

Now, summing 1+2+3+4+5+6.......+∞ = (∞+1)(∞/2) = w*(∞/2) = w +
((1/2*w)-0.5) ~(approx) w+(w/2). Therefore, 1+2.........+∞ is
NOT = -1/12.

## Successorship

Successorship is adding one to any number.

As an example, n+1.

Adding one is just moving one place to the right on a number line.

n+1 is always equal to n+((1/n)*n)

Some examples:

1.) (S)3 = 3+1 = 4

2.) (S)4 = 4+1 = 5

Using repeated successorship will grant you the opportunity to use
addition, or just repeated successorship.

## Plex count

The plex count has similar notation as log, but it is right above the exponent.

- 1 Levels
- 1.1 Level 1
- 1.2 Level 3
- 1.3 Level 4

Addition and subtraction take up this space.

Transformation from Level 1-Level 2:

Exponents, roots, logs...

Thansformation from Level 3-Level 4:

7^7^7^7^7^7^7=7th plex 7

Plexes, arc plexes...

The third plex of x is x^x^x^x.

The 4th arc plex of x is the number that you had run through 4th plex to arrive at x.

Ex. 2nd arc plex of 27 is 3.

Please comment below on shortcut math one can use to find arc plexes!

## Clifford algebra

- 1 Rules

Clifford algebra is a type of algebra characterized by the geometric product of scalars, vectors, bivectors, trivectors...etc.

Just as a vector has length so a bivector has area and a trivector has volume.

Just as a vector has direction so a bivector has orientation. In three dimensions a trivector has only one possible orientation and is therefore a pseudoscalar. But in four dimensions a trivector becomes a pseudovector and the quadvector becomes the pseudoscalar.

All the properties of Clifford algebra derive from a few simple rules.

Let

## Numbers 2

Proof that there is morw irrationals than integers.

Proof:

Suppose you did make a list (assume it is only the irrationals from
0-1). Lets give the first numbers on the list,

1:0.5743857926410654136534629...

2:0.5785605674106541650460134...

3:0.1332538518354568254625486...

4:0.0000000000000000000000000...(After one trillion digits, there
is a one)

I can create a number that in not on the list.

The first digit is 0

0.

The next is the first number's 10s on the list +1. (If it is 9,
make it a 0.)

0.6

The next is the second number's 100s on the list +1.

0.68

Then, it continues.

0.684167836728460162738462868...

The number is not on the list.

How about the 383rd number?

0.684167836728460162738462868...

It can't be since the number's 383rd digit is different from t…

## Intermediate mathematics

- 1 See also
- 2 External links
- 3 References

*Science is a wonderful thing if one does not have to earn one's living at it. One should earn one's living by work of which one is sure one is capable. Only when we do not have to be accountable to anybody can we find joy in scientific endeavor.*-Albert Einstein

This article is a continuation of Introductory mathematics

It has been known since the time of that all of geometry can be derived from a handful of objects (points, lines...), a few actions on those objects, and a small number of . Every field of science likewise can be reduced to a small set of objects, actions, and rules. Math itself is not a single field but rather a constellation of related fields. One way in which new fields are created is by …

## Math Fun II

- Evaluate , where
*y*represents his verticle distance above the ground and*x*represents horizontal distance away from the cliff, both in meters. What is the lenght of Bieber's fall?

b) What does Beethoven think of all this ( ͡° ͜ʖ ͡°) ?

## Symmetry in Mathematics

Symmetry In Mathematics

Symmetry in Mathematics Play A Great Role

If we square 11, it is very simple put 1(2*1)(12)get 121 same as square 12 put 1(2*2)(22) get 144 again for 13 we get 169 and for 14 we get 1 8 16=196 and so on.

When we go deep, we find that there is symmetry of two types

(2,4,6,8,10,12 ,14,16,18,20 …. Diff is **always 2**) &

(1, 4 , 9 ,16,25,36,49,64,81,100 ) diff. is 3 5 7 9 11 13 15 17 19
and diff. of 3 5 7 9 11 **always 2**, so there is **True
Symmetry** .

Up to 19 it is right but at 20 how we can put 1 20 100 just because of symmetry.

- 112 = 1 2 1
- 122 = 1 4 4
- 132 = 1 6 9
- 142 = 1 8 16 = 100 + 80 + 16 = 196
- 152 = 1 10 25 = 100 + 100 + 25 = 225
- 162 = 1 12 36 = 100 + 120 + 36 = 256
- 172 = 1 14 49 = 100 + 14…

## Glossary of Mathematical Terms

- 1 Definitions
- 1.1 Algebra
- 1.2 Arithmetic
- 1.3 Calculus
- 1.4 Geometry
- 1.5 Mathematics
- 1.6 Trigonometry

*n* - The study of statements of relations.

*n* - The study of numbers and their properties.

*n* - The study of change.

*n* - The study of measurement, figures, and shapes

*n* - The study of numbers, shape, space, and change.

*n* - The advanced study of triangles and angles.

## Art Of Problem Solving Wiki

Join us on Art Of Problem Solving wiki! There are tons of stuff going on! We already have 10 contributors! Become part of staff! And more! Join art of problem solving wiki, now.

Address:

art-of-problem-solving.wikia.com/wiki/Art_Of_Problem_Solving_Wiki

## Various Research Involving the Floor Function

After reading your article on Rounding, I see that you do not have much information regarding the floor function. I've been working with it on my own for a few years and recently I decided to compile my collective knowledge into one document. I would like to propose that the math wikia add some of the floor function information to the wikia. It's reasonably easy to understand (at least, in my opinion). I know it isn't really filled out too much, but let me know what you all think.

Thanks

-The Great Duck

## MATHCOUNTS

Mathcounts is a math organization created by Raytheon, Art of Problem Solving, and more!

## 4D Visualization - Higher Dimensional Space

- 1 Introduction
- 1.1 Higher-Dimensional Space
- 1.2 Why Bother?
- 1.3 Is it possible to visualize 4D?

The world around us exists in 3-dimensional (3D) space. There are 3 pairs of cardinal directions: left and right, forward and backward, and up and down. All other directions are simply combinations of these fundamental directions. Mathematically, these pairs of directions correspond with three coordinate axes, which are conventionally labelled X, Y, and Z, respectively. The arrows in the diagram indicate which directions are considered numerically positive and which are negative. By convention, right is positive X, left is negative X, forward is positive Y, backward is negative Y, and up is positive Z, and down is negative Z. We shall refer to these dir…

## Kids, don't be like me...

So I was pondering this morning? Can there be another interger other than one already existing that multiplies by another interger to give the same product. In other wrods, can the equation

Feel free to tell me how stupid I am in the comments below! :)
--Slow Reader (talk) 16:52, April 14, 2015 (UTC)

## What's the most useful thing you've used Maths for?

For me it's been every time I've completely proved someone wrong in an argument by implementing maths to justify my point. Not a lot of people understand maths to a high to degree so when I use it in an argument it tends to reult in my success. For instance, someone was being a bit christimiatic (hatred of christians) to me and was saying ti's impossible God made everything in the universe. In response I gave him a long mathematical rant of how the probability that this universe exists is so low it may as well be zreo.

What about you? Have you ever owned someone with maths? Have you used it to pull of the most awesome trick? Do you just think it's simply good for finding elegant and beutiful solutions to problems on paper? Post below! :)

--S…

## Mathematical Help

Need help on homework? Insert your questions below, and I might be able to answer right away!

If I don't answer soon enough, it means I'm really busy...

Talk to Ya Later,

-Mathematical Geek

- MATHROCKS!!!

## Integrals

**CHALLENGE:** So...I wonder who among you active high level,
math-oriented users can solve this indefinite integral. (Don't
worry, the answer might seem less intimidating than the given
:p)

Enjoy!

## Vi Hart- The Mathemusician

**Victoria Hart,** commonly
known as **Vi Hart**,
is a self-described "recreational mathemusician" who is most known
for her mathematical videos on YouTube.

*I copied the previous text from Wikipedia but the next few
lines of text would not be from wikipedia.*

Vi Hart one of the well know youtube users with 795,249 subscriptions. She's known for her interesting videos which mainly contains elements of mathematics. She can sing too!

Though you should not think of her as being deemed as a mathematician just because of her youtube channel, she has co-authored several research papers on computational geometry and mathematics of paper folding .

Her videos always motivated me to stay with maths. From the first video of Doodling in Math Class (that I saw for the…

## Primo

I found this prime number game, *Primo*, online and it
seems to be really fun and interesting.

## Mathematical Symbols.

Hey guys! I was just going through the wiki pages and blogs and have seen a lot of symbols. So I just decided to make this as a list of the symbols and their meaning for myself and others. ( I will put them up upon request and when I encounter them. )

=Equality Equals
*x *= *y* means that

≠Inequality Doesn't Equal

## Proof the Square Root of 2 is Irrational

**Axiom 1:** All rational numbers can be expressed as a
fraction of two integers.

## can you help me with my math?

Okay guy's, Im in 9th grade currently, and im failing math, if I don't pass I won't get a deploma, I have autism, (adhd and aspergers to be exact) and im really into politics and military and history, but anyways can you help me with this?

y + 3 = -25x

-1/4x - y = 4## 【1 paradox】Why 0.999... is not equal to 1?

【1 paradox】Why 0.999... is not equal to 1?

Written in 2012

The current mathematic theory tells us, 1>0.9, 1>0.99, 1>0.999, ..., but at last it says 1=0.999..., a negation of itself. So it is totally a paradox, name it as 【1 paradox】. You see this is a mathematic problem at first, actually it is a philosophic problem. Then we can resolve it. Because math is a incomplete theory, only philosophy could be a complete one. The answer is that 0.999... is not equal to 1. Because of these reasons:

1. The infinite world and finite world.

We live in one world but made up of two parts: the infinite part and the finite part. But we develop our mathematic system based on the finite part, because we never entered into the infinite part. Your attention, God i…

## LaTeX

♦ Have did you notice that the only very fine HTML-LaTeX available are math.wikia and wordpress?