OpenLLM-France/wikimedia huggingface dataset:
# Packing & Moving Household Goods/Newsprint Problems
## Beware of Newspaper Print

Newspaper print residue must be hand washed off of all things it touches; dishwasher washing will not take it off. Also, print residue can ruin porous items like clay pots or lampshades or items with a rough finish like computer equipment. Packer’s paper is newspaper without print. It can be purchased most economically at a mover’s supply warehouse and movers will also sell it to you.
One possible solution is to use clothing to wrap, protect and cover fragile items.
# Packing & Moving Household Goods/Packing Materials

The moving industry has standard sized boxes that are best to use during your move if you can get them from a local mover or moving supply house. These include wardrobes (comes with a bar across the top to hang clothes on), dish packs (for dishes!), large, medium and book cartons (small). There are also mirror/picture cartons for mirrors, pictures, glass table tops and other fragile, large, flat objects and matress cartons for matresses. Don't forget that someone has to pick the box up after you pack it - don't load heavy objects in a large carton. You may also want to use bond paper boxes from your workplace, which are good for holding books and other small heavy items. All staples in top and bottom box flaps (not the staples on one side of the box that hold it together) of other kinds of boxes should be removed so as to safeguard surfaces such as wood floors, counter tops, and furniture where cartons may be stacked prior to pickup and after delivery.
Packer’s tape is best for sealing your boxes shut but be sure to get a good grade of it because cheaper grades tend to break unexpectedly. Make sure the bottom of the box is well taped.
Use bunched up clean paper or bubble wrap to pack your fragiles. Bunched up paper is considered the best of all wrappings for cushioning as opposed to hard to handle peanuts that can shift around in the box or bubble wrap that loses its cushioning power if some of the bubbles break.
Plastic wrap is great for keeping lids on things or keeping furniture drawers or doors shut without using tape and leaving its hard to remove residue on the finish. File cabinets and big plastic storage bins are good candidates for this treatment.
# Packing & Moving Household Goods/Oil Paintings

Each oil painting should be covered over with a non-acidic clear plastic wrap and then bubble wrapped or wrapped in a paper pad, or foam wrap, and then placed in a picture box or a flattened out box, taping the ends shut once it's inside. Bubble wrap can leave impressions of the bubbles on oil paintings so be sure to use the non-acidic clear plastic wrap over the oil so that this doesn't happen.
Another option is to cover the oil painting with glassine. This is like wax paper, except a LOT larger. It is non-acidic. And it is available from most moving companies. When loading the packed Oil Paintings into a truck, keep them on their edge, do NOT lay flat, and keep closer to the floor rather than the roof where the temperatures are a lot hotter.
# Packing & Moving Household Goods/Movers safety when moving

The very most important consideration for your moving task is Mover's Safety. The following are just a few moving safety tips to protect your moving helpers…
* Always wear good waterproof shoes with firm slip resistant soles.
* Make sure your path is clear and well lighted before carrying a load.
* If possible, know where to put down a load before you even lift the load up.
* Everyone watch for and signal others of uneven surfaces which could cause tripping and / or stumbling or could cause a load to dump from a dolly.
* Never hurry when carrying a load. Take your time and if the load's heavy, set it down periodically and rest. Your strength will last longer with occasional rests.
* When carrying big furniture using 2-3-4 men be sure you can hear one another and that you all speak the same language. Use simple, short commands that can be yelled to one another when visibility is restricted like pick and set and go and stop and backup!
* Organize your work area to eliminate unnecessary redundant lifting or moving.
* If walking over snow or ice or water or over a padded glossy hardwood floor take extra care to stay balanced and to not slip.
* Keep children & pets out of the moving area.
Remember, we cannot emphasize it enough; Mover's Safety is the very most important consideration when moving yourself!
# Packing & Moving Household Goods/Moving Insurance
## Protect Your Move

No matter where you are moving to, insurance can help protect the things that you have worked so hard for over the years. Just like any other insurance policy, moving insurance takes a fee and then provides you cash payment if something is damaged while it is being moved.

## Where to Buy Moving Insurance

There are a couple of different places that consumers can purchase moving insurance from. First is the moving company itself, which offers an insurance-like product called valuation. When you choose valuation instead of traditional insurance, you will be getting a set per pound amount for each pound of goods that is being shipped. Most companies offer a basic level of valuation coverage for free with the purchase of their services, but this is usually not enough to cover the value of the items being shipped. Consumers can, however, purchase additional coverage if they choose to.
Another place to get moving insurance is a traditional insurance company. Movers are not insurance companies, so their version of moving insurance is not actual insurance. When you choose a traditional policy, however, you will be dealing with actual insurance. These policies can be purchased separately or they can be added on to your homeowners policy. They cover the cost of each item individually rather than a per pound rate.

## Things to Consider

Purchasing moving insurance is a very important part of every move. It is important that consumers think about the worth of their goods and find out how much of each type of insurance would be needed to replace everything. By doing this, consumers can guarantee that they have enough coverage.
# Linear Algebra/Computing Linear Maps

The prior section shows that a linear map is determined by its action on a basis. In fact, the equation
    $h({\vec {v}})=h(c_{1}\cdot {\vec {\beta }}_{1}+\dots +c_{n}\cdot {\vec {\beta }}_{n})=c_{1}\cdot h({\vec {\beta }}_{1})+\dots +c_{n}\cdot h({\vec {\beta }}_{n})$
shows that, if we know the value of the map on the vectors in a basis, then we can compute the value of the map on any vector ${\vec {v}}$ at all. We just need to find the $c$'s to express ${\vec {v}}$ with respect to the basis.
This section gives the scheme that computes, from the representation of a vector in the domain ${\rm {Rep}}_{B}({\vec {v}})$, the representation of that vector's image in the codomain ${\rm {Rep}}_{D}(h({\vec {v}}))$, using the representations of $h({\vec {\beta }}_{1})$, ..., $h({\vec {\beta }}_{n})$.
# Linear Algebra/Complex Representations

Recall the definitions of the complex number addition
    $(a+bi)\,+\,(c+di)=(a+c)+(b+d)i$
and multiplication.
    ${\begin{array}{rl}(a+bi)(c+di)&=ac+adi+bci+bd(-1)\\&=(ac-bd)+(ad+bc)i\end{array}}$

## Example 2.1

For instance, $(1-2i)\,+\,(5+4i)=6+2i$ and $(2-3i)(4-0.5i)=6.5-13i$.
Handling scalar operations with those rules, all of the operations that we've covered for real vector spaces carry over unchanged.

## Example 2.2

Matrix multiplication is the same, although the scalar arithmetic involves more bookkeeping.
    ${\begin{pmatrix}1+1i&2-0i\\i&-2+3i\end{pmatrix}}{\begin{pmatrix}1+0i&1-0i\\3i&-i\end{pmatrix}}$
       ${\begin{aligned}&={\begin{pmatrix}(1+1i)\cdot (1+0i)+(2-0i)\cdot (3i)&(1+1i)\cdot (1-0i)+(2-0i)\cdot (-i)\\(i)\cdot (1+0i)+(-2+3i)\cdot (3i)&(i)\cdot (1-0i)+(-2+3i)\cdot (-i)\end{pmatrix}}\\&={\begin{pmatrix}1+7i&1-1i\\-9-5i&3+3i\end{pmatrix}}\end{aligned}}$
Everything else from prior chapters that we can, we shall also carry over unchanged. For instance, we shall call the ordered set of vectors
    $\left\langle {\begin{pmatrix}1+0i\\0+0i\\\vdots \\0+0i\end{pmatrix}},{\begin{pmatrix}0+0i\\1+0i\\\vdots \\0+0i\end{pmatrix}},\dots ,{\begin{pmatrix}0+0i\\0+0i\\\vdots \\1+0i\end{pmatrix}}\right\rangle$
the standard basis for $\mathbb {C} ^{n}$ as a vector space over $\mathbb {C}$ and again denote it ${\mathcal {E}}_{n}$.
# Linear Algebra/Cramer's Rule
## Cramer's Rule

Let's try to solve the systems of linear equations: a$_{11}$x$_1$+a$_{12}$x$_2$+a$_{13}$x$_3$+...+a$_{1n}$x$_n$=b$_1$ a$_{21}$x$_1$+a$_{22}$x$_2$+a$_{23}$x$_3$+...+a$_{2n}$x$_n$=b$_2$ a$_{31}$x$_1$+a$_{32}$x$_2$+a$_{33}$x$_3$+...+a$_{3n}$x$_n$=b$_3$ ... a$_{n1}$x$_1$+a$_{n2}$x$_2$+a$_{n3}$x$_3$+...+a$_{nn}$x$_n$=b$_n$
Which is the special case when the number of equations and the number of variables are the same.
Consider the matrix
${\begin{bmatrix}a_{11}&a_{12}&a_{13}&\ldots &a_{1n}\\a_{21}&a_{22}&a_{23}&\ldots &a_{2n}\\a_{31}&a_{32}&a_{33}&\ldots &a_{3n}\\\vdots &\vdots &\vdots &\vdots &\vdots \\a_{n1}&a_{n2}&a_{n3}&\ldots &a_{nn}\\\end{bmatrix}}$
to be denoted D.
First, we multiply the nth equation by the cofactor Co(a$_{nj}$) for the jth column, and add it all up. This gets us
Co(a$_{1j}$)a$_{11}$x$_1$+Co(a$_{1j}$)a$_{12}$x$_2$+Co(a$_{1j}$)a$_{13}$x$_3$+...+Co(a$_{1j}$)a$_{1n}$x$_n$+ Co(a$_{2j}$)a$_{21}$x$_1$+Co(a$_{2j}$)a$_{22}$x$_2$+Co(a$_{2j}$)a$_{23}$x$_3$+...+Co(a$_{2j}$)a$_{2n}$x$_n$+ Co(a$_{3j}$)a$_{31}$x$_1$+Co(a$_{3j}$)a$_{32}$x$_2$+Co(a$_{3j}$)a$_{33}$x$_3$+...+Co(a$_{3j}$)a$_{3n}$x$_n$+ +...+ Co(a$_{nj}$)a$_{n1}$x$_1$+Co(a$_{nj}$)a$_{n2}$x$_2$+Co(a$_{nj}$)a$_{n3}$x$_3$+...+Co(a$_{nj}$)a$_{nn}$x$_n$ = Co(a$_{1j}$)b$_1$+Co(a$_{2j}$)b$_2$+Co(a$_{3j}$)b$_3$+...+Co(a$_{nj}$)b$_n$.
The left side cancels out except for Co(a$_{1j}$)a$_{1j}$x$_j$+Co(a$_{2j}$)a$_{2j}$x$_j$+Co(a$_{3j}$)a$_{3j}$x$_j$+...+Co(a$_{nj}$)a$_{nj}$x$_j$
which is equal to $x_{j}{\begin{bmatrix}a_{11}&a_{12}&a_{13}&\ldots &a_{1n}\\a_{21}&a_{22}&a_{23}&\ldots &a_{2n}\\a_{31}&a_{32}&a_{33}&\ldots &a_{3n}\\\vdots &\vdots &\vdots &\vdots &\vdots \\a_{n1}&a_{n2}&a_{n3}&\ldots &a_{nn}\\\end{bmatrix}}=D$
and the right side is equal to
${\begin{bmatrix}a_{11}&a_{12}&a_{13}&\ldots &b_{1}&\ldots &a_{1n}\\a_{21}&a_{22}&a_{23}&\ldots &b_{2}&\ldots &a_{2n}\\a_{31}&a_{32}&a_{33}&\ldots &b_{3}&\ldots &a_{3n}\\\vdots &\vdots &\vdots &\vdots &\vdots &\vdots &\vdots \\a_{n1}&a_{n2}&a_{n3}&\ldots &b_{n}&\ldots &a_{nn}\\\end{bmatrix}}$, to be denoted D(j), which is the same thing as D but with the jth column replaced by b$_k$.
Dividing by D gets x$_j$=${\frac {D_{j}}{D}}$.
This formula is called Cramer's Rule, and this solution exists when D is not equal to 0.
In particular, in the process of finding the solution, we also find that this is the only solution, so this solution is unique.

### Example

Consider the system of linear equations below. $3x_{1}+2x_{2}-5x_{3}=15$ $5x_{1}+x_{3}=23$ $x_{2}+x_{3}=12$
If we only want the solution for, say, $x_{2}$, we can apply Cramer's Rule to find that its solution is ${\frac {D_{2}}{D}}$, and since we know $D_{2}={\begin{bmatrix}3&15&-5\\5&23&1\\0&12&1\end{bmatrix}}$, $x_{2}={\frac {\det {\begin{bmatrix}3&15&-5\\5&23&1\\0&12&1\end{bmatrix}}}{\det {\begin{bmatrix}3&2&-5\\5&0&1\\0&1&1\end{bmatrix}}}}=9$.
# Linear Algebra/Complex Vector Spaces

This chapter requires that we factor polynomials. Of course, many polynomials do not factor over the real numbers; for instance, $x^{2}+1$ does not factor into the product of two linear polynomials with real coefficients. For that reason, we shall from now on take our scalars from the complex numbers.
That is, we are shifting from studying vector spaces over the real numbers to vector spaces over the complex numbers— in this chapter vector and matrix entries are complex.
Any real number is a complex number and a glance through this chapter shows that most of the examples use only real numbers. Nonetheless, the critical theorems require that the scalars be complex numbers, so the first section below is a quick review of complex numbers.
In this book we are moving to the more general context of taking scalars to be complex only for the pragmatic reason that we must do so in order to develop the representation. We will not go into using other sets of scalars in more detail because it could distract from our goal. However, the idea of taking scalars from a structure other than the real numbers is an interesting one. Delightful presentations taking this approach are in (Halmos 1958) and (Hoffman & Kunze 1971) harv error: no target: CITEREFHoffmanKunze1971 (help).

## References

* Halmos, Paul P. (1958), Finite Dimensional Vector Spaces (Second ed.), Van Nostrand.
* Hoffman, Kenneth; Kunzy, Ray (1971), Linear Algebra (Second ed.), Prentice-Hall.
# Neapolitan/501 Neapolitan verbs/fernì
## fernì

* to stop, finish
1. Innecativo
    a. presente
       io fernesco tu fernisce isso/essa fernesce nuje fernimmo vuje fernite isse/lloro fernesceno
Participio passato
       fernuto
# Neapolitan/501 Neapolitan verbs/jucà

English- To play
Italiano- Giocare
# Neapolitan/501 Neapolitan verbs/mpazzì

English- To go mad
Italiano- Impazzire
# Neapolitan/501 Neapolitan verbs/parlà

to talk, to speak
# Neapolitan/501 Neapolitan verbs/penzà

English- To Think
Italiano- Pensare
# Neapolitan/501 Neapolitan verbs/fà

fà
* English: to do, make
* Italian: fare
To form the compound tenses add the auxiliary verb (avé) + past participle (fatto)
1. Indicativo
    a. presente
       io faccio (facc') tu faje (fa') isso/essa fa nuje facímmo vuje facíte isse/lloro fanno
    b. mperfetto
       io facevo tu facive isso/essa faceva nuje facevamo vuje faciveve isse/lloro facevano
    c. passato remoto
       io facétte tu faciste isso/essa facétte nuje facéttemo vuje facisteve isse/lloro facéttero
    d. futuro sémprece
       io faciarràggio tu faciarràje isso/essa faciarrà nuje faciarràmmo vuje faciarràte isse/lloro faciarrànno
2. Cungentivo
    a. mperfetto
       io fasse, facesse tu fasse, facisse isso/essa fasse, facesse nuje fassemo, facessemo vuje fasseve, facisseve isse/lloro fasseno, facesseno
3. Cundiziónale
    a. presente
       io farría, faciarrìa tu farrísse, faciarrìsse isso/essa farría, faciarrìa nuje farríamo, faciarrìamo vuje farrísseve, faciarrìsseve isse/lloro farríano, faciarrìano
4. 'Mperativo
    a. presente
       tu fa, faje nuje facimmo vuje facite
5. Participio passato
       fatto
6. Gerunnio
       facenno
# Neapolitan/501 Neapolitan verbs/fuì

To escape
# Neapolitan/501 Neapolitan verbs/natà
## natà

* English- to swim
* Italian- nuotare
To form the compound tenses add the auxiliary verb (avé) + past participle (natato)
1. Indicativo
    a. presente
       io nato tu nate isso/essa nata nuje natammo vuje natate isse/lloro natano
    b. mperfetto
       io natévo tu native isso/essa natéva nuje natévamo vuje nativeve isse/lloro natévano
    c. passato remoto
       io natétte tu natiste isso/essa natétte nuje natéttemo vuje natisteve isse/lloro natéttero, carétteno
    d. futuro sémprece
       io natarràggio tu natarràje isso/essa natiarrà nuje natiarràmmo vuje natiarràte isse/lloro natiarrànno
2. Cungentivo
    a. mperfetto
       io natésse tu natisse isso/essa natésse nuje natéssemo vuje natisseve isse/lloro natésseno
3. Cundiziónale
    a. presente
       io natarrìa tu natarrìsse isso/essa natarrìa nuje natarrìamo vuje natarrìsseve isse/lloro natarrìano
4. 'Mperativo
    a. presente
       tu nata vuje natate
5. Participio passato
       natato
6. Gerunnio
       natanno
# Neapolitan/501 Neapolitan verbs/dà

English- To give
Italiano- Dare
# Neapolitan/501 Neapolitan verbs/ghì
## ghì

Also, jì, ì, annare
    to go
1. Innecativo
    a. presente
       io vaco (vac') tu vaje (va') isso/essa va nuje jammo vuje annate or jate isse/lloro vanno
    b. mperfetto
       io jevo tu jive isso/essa jeva nuje jevemo vuje jiveve isse/lloro jeveno
    c. passato remoto
       io jette tu jiste isso/essa jette nuje jettemo vuje jisteve isse/lloro jetteno
    d. futuro sémprece
       io jarraggio tu jarraje isso/essa jarrà nuje jarrimmo vuje jarrite isse/lloro jarranno
2. Cungiuntivo
    a. mperfetto
       io jesso tu jissi isso/essa jesse nuje jessemo vuje jistene isse/lloro jesseno
3. Cundizionale
    a. presente
       io jarria tu jarrisse isso/essa jarria nuje jarrissemo vuje jarrissevo isse/lloro jarriano
4. Mperativo
    a. presente
       tu va vuje jate
5. Participio passato
       ghiuto or juto
6. Gerunnio
       ghienno or jenno
# Pinyin/Compared To

See also
# Pinyin/Community

Search Pinyin community
# Pinyin/Company

A company is a business organization that makes money by producing or selling goods or services.
gongsi shih tongguoh shengchaan, maaimaih huoh furwuh zhuahnqiarn d shangyeh jigouh.
# Pinyin/Complete

See also
# Pinyin/Communication

Communication is the activity or process of expressing ideas and feelings or of giving people information.
goutong shih biaaodar yihjiahn her gaanshouh huoh fenxiaang xihnxi d huordohng huoh gouhcherng.
# Mathematical Proof/Appendix/Answer Key/Mathematical Proof/Methods of Proof/Counterexamples

(Q).Using the method of induction,show that for all n € N,
Soln: Let us take
When,n=1,then , L.H.S.=n , R.H.S.=n(n+1)/2
.°. L.H.S.=R.H.S,so,the statement given is true for n=1
Let,the statement be true for n=k i.e.S(k)=>1+2+3+....+k=k(k+1)/2(i)
Again,Let the statement be true for n=k+1 i.e=>1+2+3+....+k+(k+1)=(k+1)(k+1+1)/2
.i.e.=>1+2+3+....+k+(k+1)=k(k+1)/2+(k+1)
Hence,the statement given for n=k+l is also true.
So,it is true for all n € N
# Mathematical Proof/Appendix/Answer Key/Mathematical Proof/Methods of Proof/Proof by Contrapositive

a$^3$+b$^3$=(a+b)(a$^2$-ab+b$^2$)
# Mathematical Proof/Appendix/Answer Key/Mathematical Proof/Introduction/Notation

These are the answers to the exercises in section 1.2, Notation
* Use set theory notation
** $P\cap L$, where P is the set of all people and L is the set of all things with two legs.
** $M-G$, where M is the set of all mythological creatures and G is the set of all things that are Greek.
** $A\cap B-C$, where A is the set of all pies, B is the set of all things with pudding in them, and C is the set of all things with cream on the top.
* Venn Diagrams
* Negated statements
** $\exists x\in A:\forall y\in B,\lnot P(x,y).$
** There is a quick, brown fox that does not jump over any lazy dog.
# Mathematical Proof/Appendix/Answer Key/Mathematical Proof/Methods of Proof/Constructive Proof
### Problem 1

First, we wish to show that $A\cup (B\cap C)\subset (A\cup B)\cap (A\cup C)$. Let $x\in A\cup (B\cap C)$. Then $x\in A$ or $x\in B\cap C$.
Case 1: $x\in A$
$x\in A\subset A\cup B$ so that $x\in A\cup B$ $x\in A\subset A\cup C$ so that $x\in A\cup C$ $x\in A\cup B$ and $x\in A\cup C$ so that $x\in (A\cup B)\cap (A\cup C)$
Case 2: $x\in B\cap C$
$x\in B$ and $x\in C$ $x\in B\subset A\cup B$so that $x\in A\cup B$ $x\in C\subset A\cup C$ so that $x\in A\cup C$ $x\in A\cup B$ and $x\in A\cup C$ so that $x\in (A\cup B)\cap (A\cup C)$
Since in both cases, $x\in (A\cup B)\cap (A\cup C)$, we know that $A\cup (B\cap C)\subset (A\cup B)\cap (A\cup C)$
Now we wish to show that $(A\cup B)\cap (A\cup C)\subset A\cup (B\cap C)$. Let $x\in (A\cup B)\cap (A\cup C)$. Then $x\in A\cup B$ and $x\in A\cup C$.
Case 1a: $x\in A$
$x\in A\subset A\cup (B\cap C)$, so $x\in A\cup (B\cap C)$
Case 1b: $x\in B$
We can't actually conclude anything we want with just this, so we have to also to consider the case $x\in A\cup C$.
Case 2a: $x\in A$ : [see Case 1a]
Case 2b: $x\in C$
We now have $x\in B$ and $x\in C$ so that $x\in B\cap C$ Of course, since $x\in B\cap C\subset A\cup (B\cap C)$, it follows that $x\in A\cup (B\cap C)$. Since both cases 2a and 2b yield $x\in A\cup (B\cap C)$, we know that it follows from 1b.
Since in both cases 1a and 1b, $x\in A\cup (B\cap C)$, we know that $(A\cup B)\cap (A\cup C)\subset A\cup (B\cap C)$.
Since both $A\cup (B\cap C)\subset (A\cup B)\cap (A\cup C)$ and $(A\cup B)\cap (A\cup C)\subset A\cup (B\cap C)$, it follows (finally) that $A\cup (B\cap C)=(A\cup B)\cap (A\cup C)$.
--will continue later, feel free to refine it if you feel it can be--

### Problem 3

* Because the question asks about the square of a number, you can substitute the definition of an odd number 2n + 1 into the number to be squared. So, say x is that number, then$x^{2}=(2n+1)^{2}=(2n+1)(2n+1)$
* Multiply both factors together $(2n+1)(2n+1)=4n^{2}+4n+1$
* Factor out a two for the first two terms $4n^{2}+4n+1=2(2n^{2}+2n)+1$
* The factor $2n^{2}+2n$ will always be a natural number. As such, it fits the definition of an odd number, 2n + 1
    Problem solved!
# Mathematical Proof/Appendix/Symbols Used in this Book

This is a list of all the mathematical symbols used in this book.
$[a,b]$
       Closed interval notation. Signifies the set of all numbers between a and b (a and b included)
$\lor$
       A logical "or" connector. A truth statement whose truth value is true if either of the two given statements is true and false if they are both false. $P\lor Q$
$\land$
       A logical "and" connector. A truth statement whose truth value is true only if both of the two given statements is true and false otherwise. $P\land Q$
$\lnot$
       A logical "not" unary operator. A truth statement whose value is opposite of the given statement. $\lnot P$
       Set delimiters. A set may be defined explicitly (e.g. $A=\{1,2,3,4\}$), or pseudo-explicitly by giving a pattern (e.g. $B=\{2,4,6,8,\ldots \}$. It may also be defined with a given rule (e.g. $C=\{x|P(x)\}$, the set of all x such that P(x) is true).
$\in$
       The "element of" binary operator. This shows element inclusion in a set. If x is an element of A we write $x\in A.$
$\subset$
       The "set inclusion" or "subset" binary operator. If all the elements of A are in B, then we say that A is a subset of B and write $A\subset B.$ Note that in this book, $A\subset B$ when $A=B.$
$\cup$
       The union of two sets. A set containing all elements of two given sets. $A\cup B=\{x|(x\in A)\lor (x\in B)\}.$
$\cap$
       The intersection of two sets. A set containing all the elements that are in both of two given sets. $A\cap B=\{x|(x\in A)\land (x\in B)\}.$
# Mathematical Proof/Introduction

If you've ever taken a math class or talked to a mathematician, you know that we don't talk like normal people do--we have our own language that's 2-bit encoded. For example, when a waiter says "Would you like corn or beans with your dinner?", you know that he wants the answer of "corn" or "beans" but not "both". Well, logically, if you ask the question "Would you like corn or beans with your dinner?", the answer could be "yes".
This chapter will acquaint you with logical statements, logical reasoning, and the cryptic language of mathematicians.