User:CaritasUbi/sandbox

This is the user sandbox of CaritasUbi. A user sandbox is a subpage of the user's user page. It serves as a testing spot and page development space for the user and is not an encyclopedia article. Create or edit your own sandbox here.

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Test[edit]

Scratch pad - no need to create unnecessary subpages.

Tables[edit]

Name	Rank	Saying
Moe	1	"Why, I oughta..."
Larry	2	"Owwwww"
Curly	"Nyuk, nyuk, nyuk"

Math[edit]

Quadratic Equation[edit]

The general solution to the quadratic equation $ax^{2}+bx+c$ is $x=(-b\pm {\sqrt {b^{2}-4ac}})/2a$

Conditional Probability[edit]

Theorem 1: For all events A and B, $P(A\mid B)+P(A\mid {\bar {B}})=P(A)$

Proof: Assert that event A happens, and denote the probability of this event as $P(A)$ . If the probability that $B$ happened is $P(B)$ , then the probability that $B$ did not happen is $P({\bar {B}})=1-P(B)$ , because these two events encompass *all* the possibilities (by the Law of the Excluded Middle). Thus, the probability of blah, blah, blah, finish me.

More math[edit]

Theorem 1: Every function with a left inverse is injective.

Proof: Let $f:X\to Y$ be a function and suppose that f has a left inverse $g:Y\to X$ . That is, if $f(x)=y$ , then $g(y)=x$ . To say that f is injective, we need to show that $f(a)=f(b)$ can be true if and only if $a$ and $b$ are the same number.

Given any two elements $a,b\in X$ , suppose that $f(a)=f(b)=c$ . Then since f has a left inverse g, we have $g(c)=a$ and $g(c)=b$ . By this we immediately conclude that a = b, and so f is an injective function. $\Box$ .

Citiation[edit]

Example from http://toolserver.org/~verisimilus/Scholar/Cite.php^[1]

Example from http://toolserver.org/~magnus/makeref.php^[2]

Newspaper article example^[3]

References[edit]

^ Greenberg, Day W., NU professor's Russian literature lectures sold by Teaching Company, retrieved 2009-06-13
^ Greenberg, Day W. "NU professor's Russian literature lectures sold by Teaching Company". Retrieved 2009-06-13.
^ Thumb, Tom (2009-06-13). "Wikipedia author researches citation tools". New York Times. {{cite news}}: |access-date= requires |url= (help); Cite has empty unknown parameter: |coauthors= (help)

Manually formatted:

Greenberg, Day W. NU professor's Russian literature lectures sold by Teaching Company, retrieved on 2009-06-13

Quotes[edit]

"Все счастливые семьи похожи друг на друга, каждая несчастливая семья несчастлива по-своему"
(All happy families are alike; each unhappy family is unhappy in its own way.)
— Tolstoy, first line of Anna Karenina

Templates[edit]

My Labrador Abby is the best dog in the world ^{[citation needed]}.

Russian[edit]

	Singular	Plural
1st person	я бу́ду	мы бу́дем
2nd person	ты бу́дешь	вы бу́дете
3rd person	он бу́дет	они бу́дут

Instrumental case[edit]

For masculine nouns, add -ом/-ём/ем, for example, Иван Иванович becomes Иваном Ивановичем.

Images[edit]

[Greenberg-1] Greenberg, Day W., NU professor's Russian literature lectures sold by Teaching Company, retrieved 2009-06-13

[2] Greenberg, Day W. "NU professor's Russian literature lectures sold by Teaching Company". Retrieved 2009-06-13.

[3] Thumb, Tom (2009-06-13). "Wikipedia author researches citation tools". New York Times. {{cite news}}: |access-date= requires |url= (help); Cite has empty unknown parameter: |coauthors= (help)

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