Turbo C++ for Windows

Turbo C++ for Windows

http://indiaexam.in/data/misc/turboc.zip

Calcutta university 3rd year Envs fieldwork report

Calcutta university 3rd year ENVS fieldwork report
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What is Infinity?

 

Infinity ...
	... it's not big ...
	... it's not huge ...
	... it's not tremendously large ...
	... it's not extremely humongously enormous ...
	... it's ...

Endless!

Infinity is not a real number

Infinity is not a real number, it is an idea. An idea of something without an end.
Infinity cannot be measured.
Even these faraway galaxies can't compete with infinity.

Here are some more properties:

Special Properties of Infinity
∞ + ∞ = ∞
-∞ + -∞ = -∞
∞ × ∞ = ∞
-∞ × -∞ = ∞
-∞ × ∞ = -∞
x + ∞ = ∞
x + (-∞) = -∞
x - ∞ = -∞
x - (-∞) = ∞
For x>0 :
x × ∞ = ∞
x × (-∞) = -∞
For x<0 :
x × ∞ = -∞
x × (-∞) = ∞

Undefined Operations

All of these are "undefined":

"Undefined" Operations
0 × ∞
0 × -∞
∞ + -∞
∞ - ∞
∞ / ∞
∞0
1∞

Example: Isn't ∞ / ∞ equal to 1?
No, because we really don't know how big infinity is, so we can't say that two infinities are the same. For example ∞ + ∞ = ∞, so

∞	=	∞ + ∞	which would mean that:	1	=	2
∞		∞		1		1

And that doesn't make sense!
I could have also made 1=3 and so on ... so we say that ∞ / ∞ is undefined.

Pronunciation Guide to Mathematicians Name

Pronunciation Guide to Mathematicians

Abel, Niels Henrik (1802-1829) (Ä bul)
Agnesi, Maria Gaetana (1718-1799) (an YAY zee)
Banach, Stefan (1892-1945) (BÄ näkh)
Berkeley, George (1685-1753) (BÄRK lee)
Bernoulli, Jakob/Jacques/James (1654-1705)(ber NOO lee)
Bernoulli, Johann/Jean/John (1667-1748) (ber NOO lee)
Bolzano, Bernhard (1781-1848) (bolt SÄ no)
Bolyai, János (1802-1860) (BOY AY)
Cauchy, Augustin-Louis (1789-1857) (ko SHE)
Cavalieri, Bonaventura (1598-1647) (kä val YAY ree)
Clairaut, Alexis-Claude (1713-1765) (kla ROW, as in row your boat)
d'Alembert, Jean Le Rond (1717-1783) (DÄ lam bâr)
Dedekind, Richard (1831-1916) (DA de kint)
Desargues, Girard (1591-1661) (day ZÄRG)
Descartes, Rene (1596-1650) (day CÄRT)
Dirichlet, Peter Lejune (1805-1859) (dee ree KLAY)
Euclid (YOU klid)
Eudoxus (408-355 B. C.) (you DOK sis)
Euler, Leonhard (1707-1783) (OI ler)
Fermat, Pierre de (1601-1655) (fer MÄ)
Fourier, Jean Baptiste Joseph (1768-1830) (foo RYAY)
Galois, Evariste (1811-1832) (gal WÄ)
Heine, Eduard (1821-1881) (HI na, not a long a)
Hermite, Charles (1822-1901) (er MEET)
Jordan, Camille (1838-1922) (abstract algebra) (zhâr DÄN)
Jordan, Wilhelm (1842-1899) (Gauss-Jordan Elimination) (your DÄN)
Kovalevskaya, Sofia (1850-1891) (kov a LEF skä yä)
Kronecker, Leopold (1823-1891) (KROW nek er)
Kummer, Ernst (1810-1893) (KUM er)
Lagrange, Joseph Louis (1736-1813) (la GRÄNZH)
Laplace, Pierre-Simon de (1749-1827) (la PLAS)
Lebesgue, Henri (1875-1941) (la BEG)
Lie, Sophus (1842-1899) (LEE)
Legendre, Adrien-Marie (1752-1833) (la ZHÄN dra)
Leibniz, Gottfried Wilhelm (1646-1716) (LIP nits, long i)
l'Hospital, Guillaume Francois (1661-1704) (lô pee TAL)
Monge, Gaspard (1746-1818) (MÔNZH)
Napier, John1550-1617) (NAY pee air)
Noether, Emmy (1882-1935) (NOO ta)
Peano, Guiseppe (1858-1932) (pay Ä no)
Poincaré, Henri (1854-1912) (pwan ka RAY)
Another Poincaré link
Riemann, Bernhard (1826-1866) (REE män)
Sylow, Ludwig (1826-1866) (SEE lov)
Thales (THAY leez)
Torricelli, Evangelista (1608-1647) (tor ree CHEL lee)
Weierstrass, Karl (1815-1897) (vi er shträs, long i)

Symbols

Some symbols in no particular order: (Some symbols did not convert properly, will try to fix them.)

~         tilde

*          asterisk

+         plus sign

-           hyphen, minus sign

±         plus or minus

∓         minus or plus

×         multiplication sign

÷         division sign

•          dot or bullet product

∘          ring operator

=         equals

≡         is identical to

≠         is not equal to

≅         is approximately equal to

≈         almost equal to

≐         is nearly equal to

<         less than

>         greater than

≤         less than or equal to

≥         greater than or equal to

Ú        much less than

ä        much greater than

/          slash, solidus, virgule, division

\          reverse slash, solidus, set minus

|           vertical line

‖          double vertical line, parallel

∅         empty or null set

ℏ         h-bar (Planck constant over two pi)

ℕ         natural numbers

ℙ         prime numbers

ℤ         integers

ℚ        rational numbers

ℝ         real numbers

ℂ         complex numbers

ℍ        quaternions (after Hamilton)

𝕆       octonions

ℜ         real part

ℑ         imaginary part

dx       differential of x

Δx       increment of x

∂          partial derivative

∫         integral

∬        double integral

∭      triple integral

∮         contour integral

∯        surface integral

∰      volume integral

(          left parenthesis

)          right parenthesis

 [ ]       left and right square brackets

{ }        curly brackets or braces

⟨ ⟩        angle brackets

⟦ ⟧       double brackets

         floor brackets

         ceiling brackets

‖ ‖      double vertical line brackets   

∊         is a member of

⊂       is contained in

∩         cap, intersection

∪         cup, union

∨         or

∧       and

→      arrow, implies

⇒      double arrow, if then

⋯      ellipsis

!         exclamation point, factorial

         factorial (old notation)

∞      infinity

∝       proportional to

∀       for all

∃       there exists

∄         there does not exist

→      therefore

∵         because

         perpendicular

𝔃̅ or 𝔃*          complex conjugate

ℜ, Re real part

ℑ, Im imaginary part

%      per cent

‰      per mille

$        Dollar

£          Pound (British)

€       Euro

¥       Yen

Å       Angstrom

∇       del or nabla

∇²       Laplacian operator

∑       sum

∏       product

∶           ratio

∷         proportion

∝         is proportional to

&       ampersand

℃        degrees Celsius

℉        degrees Fahrenheit

.           decimal point

°           degrees

9           minutes

0           seconds

lb        pound(s)

Hz     hertz

ℵ         alef

ℵ₀      alef null, naught, or zero

ℶ        bet

ℷ        gimel

ℸ        dalet

à     Weierstrass p

|x|      absolute value of x

[x] or ⟦x⟧    integral part of x

x|y     x divides y

√       square root

∛         cube root

∠       angle

 ͞͞͞ ͞ ͞      vinculum above

___     vinculum below

         horizontal fraction bar

℄         center line symbol

†          dagger

℈         scruple

≀          wreath product

A X B          inner, vector, or cross, product

A ∙ B outer, scalar, or dot, product

■                    end of proof

QED               end of proof

BT & MB SEM-IV Model Question Paper of COMPUTER CA-401

BT & MB SEM-IV Model Question Paper of COMPUTER CA-401
http://www.mediafire.com/view/?7yol42jc4h7l01e

BBA SEM-II Model Question Paper of MATH & STAT

 BBA SEM-II Model Question Paper  of STAT
http://www.mediafire.com/view/?qaq9w2myu2212qu

BBA SEM-II Model Question Paper  of MATH
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calcutta university 3rd year Envs fieldwork report

Calcutta university 3rd year Envs fieldwork report
http://www.mediafire.com/download/7gjc40015m5jlij/New_folder.rar