saying mathsversiwords

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Saying math - Foreword

General remarks

• Individual mathematicians often have their own way of pronouncing mathematicalexpressions and in many cases there is no generally accepted "correct"

pronunciation.

• Distinctions made in writing are often not made explicit in speech (this happens

also in Italian!): for instance while and are completely differentmathematical expressions, they all sound as "the square root of a plus b" . The

difference is usually made clear by the context, but to avoid misunderstandings you

may emphasise the difference using longer expressions or different intonations andlength of pauses. The previous example can be read as "the square root of a

-pause- all plus b" (longer expression) or "the square root of a -pause- plus b",

for the first expression, and "a+b all under the square root " or "the square root of

-pause- a plus b", for the second expression. Observe the shifting of the -pause-.

Directions

• The "saying" part of a formula is always written in italics.

• The division bar ( / ) is used to keep apart different ways of saying the same

formula.

• Parentheses are used for optional parts.

• We never use commas to indicate a pause in the "saying" part of the formula, but

the explicit indication: -pause-, as in the above examples.

• Some entries can find a place in different headings: we have chosen what is more

appropriate in our opinion.

Thanks to Maria Bortoluzzi, Laura Cimetta and Mariateresa Esposito for their

invaluable help!



Saying math 1 - The Greek alphabet

As the Greek alphabet is extensively used in mathematical formulas we give in this page a

table with all letters, the English names, the pronunciation, taken from Collins English

Dictionary - Millennium Edition, and the English equivalent.

The pronunciation is written using the International Phonetic Alphabet (IPA).

We have added a column with the key used on PC keyboards under Windows Operating

System (Symbol font) to obtain the letter.

CapitalLow-

case

English

namePronunciation

English

equivalent

Keyboard

(Symbol font)

Α α alpha a A , a

Β β beta b B , b

Γ γ gamma g G , g

Δ δ delta d D , d

Ε ε epsilon e E , e

Ζ ζ zeta z Z , z

Η η eta h H , h

Θ θ ( ) theta th Q , q (J)

Ι ι iota i I , i

Κ κ kappa k K , k

Λ λ lambda l L , lΜ μ mu m M , m

Ν ν nu n N , n

Ξ ξ xi (-pl. xis) x X , x

Ο ο omicron o O , o

Π π pi (-pl. pis) p P , p

Ρ ρrho (-pl.rhos)

r R , r

Σ σ ς sigma s S , s (V)

Τ τ tau t T , tΥ υ upsilon u U , u

Φ (φ) phi (-pl.

phis) ph F , f (j)

Χ χ chi ch - kh C , c

Ψ ψ psi ps Y , y

Ω ω omega o W , w

Taken from: http://www.batmath.it/eng/say/say.htm2



Saying math 2 - Mainly numbers

Numbe rs: general remarks | Numbers: elementary calculations | Numbers: advanced calculations |Useful expressions

Numbers: general remarks

• A point (.) is used for decimals, and not a comma (,); commas in figures are

used only when writing thousands (example 10,000: ten thousand), but we prefer to avoid the use of commas in mathematical formulas.

• Use of "and"

o to indicate the location of the decimal point: so 100.5 is one

hundred and 5 tenths, but one hundred point five is by far more common;

239.36 is two hundred thirty-nine and thirty-six hundredths, but two

hundred thirty-nine point three six is by far more common;

o in British English we use and when saying numbers in the hundreds:

105 is one hundred and five;

o in American English we do not use and when saying numbers in thehundreds: 105 is one hundred five;

o anyhow we have also found on the Internet something like this: 105

is hundred five;

o so, as what is "correct" changes with time, choose your standard and

follow it!

• The "0" (oh, nought, zero, love, nil)

o oh

after the decimal point: 27.05 is twenty-seven point oh five;

in years: 1907 is nineteen oh seven;

in telephone, bus, hotel room numbers (but this is not very

important in maths!);o nought

before the decimal point: 0.05 is nought point oh five (but

see also the next heading);

tip: noughts and crosses is a game like the Italian "filetto";

o zero

for the number 0 itself: "0" is zero;

before a decimal point, mainly in American English, but also

in British English: 0.05 is zero point oh five, instead of the more"traditional" form "nought point oh five";

for the temperature: -7°C is seven degrees below zero, which

you can also say minus seven;o nil

in football scores: "Italy wins 3-0" is "Italy wins three nil "

(also three to nil ); sometimes nothing is used in the place of nil "3-0" can be three to nothing ;

o love

in tennis games: "the score of the game is 15-0" is "the scoreof the game is fifteen love"; "0-0" is love all or love game.


http://www.batmath.it/eng/say/say2.htm#Numbers%23Numbers

http://www.batmath.it/eng/say/say2.htm#elementary%23elementary



http://www.batmath.it/eng/say/say2.htm#advanced%23advanced


http://www.batmath.it/eng/say/say2.htm#Useful%23Useful

http://www.batmath.it/eng/say/say2.htm#Numbers%23Numbers



http://www.batmath.it/eng/say/say2.htm#Useful%23Useful



• The decimal point

o the numbers after the decimal point are all read separately 0.0023 is

nought point oh oh two three; use of "and" is also allowed (see the

previous heading), but we prefer this way of saying numbers with a

decimal point;o you can also use shorter forms: 0.0005 can be read as nought point

double oh oh five;o in periodic numbers we use "recurring": 5.376666... is five point

three seven -pause- six recurring , while 5.376376376... is five point

three seven six -pause- all recurring ;

o digits after the decimal point are (almost) always grouped while

reading currencies, lengths, and other measures:

£15.50 is fifteen pounds fifty / fifteen pounds fifty pence / fifteen fifty (if no misunderstanding can occur);

€2.27 is two euro twenty-seven / two euro twenty-seven

cents;

47.99s (seconds) is forty seven seconds ninety-ninehundredths;

3.87m (meters) is three meters eighty-seven centimetres.

• Kinds of numbers

o natural, whole, integer, rational, irrational, real, complex

(imaginary)

o odd, even

o fractional

o prime

o binary, octal, decimal, hexadecimal

o random

Numbers: elementary calculations

= The equals sign

x=3 ; x≠3 x equals three / x is equal to three ; x (is) not equal to three

x≡y x is equivalent to (or identical with) y

x>y ; x≥y x is greater than y ; x is greater than or equal to y

x<y ; x≤y x is less than y ; x is less than or equal to y

x<a<ya is greater than x and less than y / a is between x and y / x is less than a

and less than y

x≤a≤y

a is greater than or equal to x and less than or equal to y / a is between x

and y -pause- bounds included / x is less than or equal to a and less than

or equal to y

<< ; >> ; <<<

; >>>

much less than ; much greater than ; very much less than ; very much

greater than (The last two are not frequently used, but they are in the set of

Unicode characters).




a+b=s

(addition)

a and b are the addends, s is the sum, a and b are also the items of the

addition.

a+b=s

a plus b is ( / equals / is equal to) s

a and b is ( / equals / is equal to) s

s is the sum of a and ba-b=d

(subtraction or

difference)

a is the minuend , b is the subtrahend , d is the remainder or the

difference

a-b=d

a minus b is ( / equals / is equal to) d

a take away b is ( / equals / is equal to) d

d is the difference between a and b

a±b a plus or minus b

a×b=p, or a·b=p,or simply ab=p

(multiplication)

a and b are the factors or the multipliers, p is the product

a×b=p, or a·b=p,or simply ab=p

a times b is ( / equals / is equal to) p

a multiplied by b is ( / equals / is equal to) p

a by b is ( / equals / is equal to) p

a b is ( / equals / is equal to) p

p is the product of a and b

a : b = q, or a / b =

q (division)a is the dividend , b is the divisor , q is the quotient or the ratio

a:b=q, or a/b=q

a divided by b is ( / equals / is equal to) q

q is the quotient of the division of a by b

verbs concerning

operationsto sum, to subtract / to deduct, to multiply, to divide

(fraction)

a is the numerator , b is the denominator (the outcome is always called

the quotient , as in the division)

a fraction can be said a divided by b (as a normal division ), or a over b.

Cardinal numbers for the numerator and ordinal numbers for the

denominator are also used (as in Italian): is a third , is two thirds.

Special cases are (a/one half ), (a/one quarter ), (three halves),

(three quarters), and similar. The special notation sometimes used

for improper fractions, as , is said three and a half .




Numbers: advanced calculations

|x| or abs(x) The absolute value of x

a b a is the base, b is the index or the exponent

x2

x squared / x (raised) to the power two

x3 x cubed / x (raised) to the power three

x4 x to the fourth / x (raised) to the power four

xn x to the nth / x (raised) to the power n

x-n x to the minus n / x (raised) to the power minus n

root x / square root x / square root of x

cube root x / cube root of x

fourth root x / fourth root of xnth root x / nth root of x

nth root -pause- x cubed or nth root -pause- of x cubed

x hat

x bar

x tilde

x dot

x dot dot / x double dot

n! n factorial / factorial n

n choose p

xi x i / x subscript i / x suffix i / x sub i

xi (not a power!) x index i / sometimes x i if no misunderstanding with xi can occur / x superscript i

(x+y)3 ; (x+y)n x plus y all cubed ; x+y all to the nth

x3+y3 x cubed plus y cubed

a1 + a2 + ... +an a one plus a two and so on up to a (sub) na1 × a2 × ... ×an a one times a two and so on up to a (sub) n

the summation symbol

the sum as i runs from zero to n of the x i / the sum from i equals zero

to n of the x i




the sum -pause- as i runs from one to n -pause- of the quantity n

over 3 -pause- plus the quantity 2 over n -pause- all squared (but

probably nobody will understand what you mean if he can't read the blackboard or the transparency!!)

parenthesis -pl. parentheses / round brackets

brackets / square brackets

braces / curly brackets

π pi

Useful expressions

• the noughts and ones of computer language: to refer to the digits used by

computers ("0" and "1")• the slashed zero: the zero of the computer

• to reset to zero

• to extract a root

• to cast out nines (the famous test for divisions)

• to move the decimal point back (or forward) two places

• readings accurate to two decimal places

• to round a number up or down to the nearest integer

• to calculate up to n decimal places

• to reduce to the lowest common denominator




Saying math 3 - Logic and Sets, Functions

Logic and sets

there exists

! there exists only one

p non p / not p

| such that (in the definition of sets by listing)

for all / for any

p q p implies q / if p then q

p q p if and only if q / p is equivalent to q / p and q are equivalent

x A x is an element of A / x belongs to A

x A x is not an element of A / x does not belong to AU universal set

empty set

A B A is (properly) contained in B / A is a (proper) subset of B

A B A (properly) contains B / B is a (proper) subset of A

A ∩ B A intersection B / A meet B / A cap B

A B A union B / A join B / A cup B

A \ B A minus B / the difference between A and B

Ac or the complement of A

A × B A cross B / the Cartesian product of A and B

P (A)= {0,1}Athe power set of A / the set of all subsets of a set A

(a,b) the ordered pair a b

Functions and analysis

ex e to the x / the exponential function

lnx natural logarithm of x / natural log of x / log base e of x / ln of x

ax a to the x / the exponential function base a

logax log base a of x / log x base a

sinx sine x / sine of x




cosx cosine x / cosine of x

tanx tangent x / tangent of x

arcsinx arcsine x / arcsine of x / inverse sine of x

arccosx arccosine x / arccosine of x / inverse cosine of x

arctanx arctangent x / arctangent of x / inverse tangent of x

f : S → T function f from S to T

S is the domain, T the range (rarely the codomain)

f(A) ; f(X)

the image of A ; the image of the domain or simply the image

(observe that, as in Italian, there is no general agreement about these

terms: range is often used in the place of image - we do not agree withthis)

f -1(B) the inverse image of B / the pre-image of B

f : x y f maps x to y

x y x maps to y / x is sent ( or mapped) to y

f(x) f x / f of x / the function f of x

f -1(x) f inverse -pause- of x

f ' f prime / f dash / the derivative of f / the first derivative of f

f '(x) f prime (of) x / f dash (of) x / the derivative of f with respect to x / the first

derivative of f with respect to x

f '' f double-prime / f double-dash / the second derivative of f

f ''(x) f double-prime (of) x / f double-dash (of) x / the second derivative of f

with respect to x

f ''' ; f '''(x)the same as f ' or f '(x) with triple-prime or triple-dash in the place of

prime or dash

f (n) f n / the nth derivative of f

f (n)(x) f n (of) x / the nth derivative of f with respect to x

d f d x / see f '

d squared f -pause- (over ) d x squared / see f'' or f''(x)

limit as x tends to c of f x / limit as x approaches c of f x

... tends to c from above... / ... approaches c from above ...

... tends to c from below... / ... approaches c from below ...

∞ ; +∞ ; -∞ infinity (while infinite is an adjective) ; plus infinity ; minus infinity




limit as x tends to infinity of f x / limit as x goes to infinity of f x

the indefinite integral of f x d x / the antiderivative of f x

the definite integral of f x d x from a to b

the (first) partial derivative of f with respect to x1

the second partial derivative of f with respect to x1

Terms about

functions

surjection / surjective map / onto map

injection / injective map

bijection / bijective map / one-to-one map

composition map

piecewise defined map




Saying math 4 - Linear Algebra and Analytic Geometry

Matrices

the norm of x

AT A transpose / the transpose of A

A-1 A inverse / the inverse of A

Terms about matrices

determinant minor

cofactor

adjoint upper triangular

lower triangular

diagonal

Analytic geometry

Systems of coordinates

cartesian

polar

cylindric / cylindrical

spheric / spherical

Operations with systems of

coordinates

translation

rotation

scaling

mirroring / reflection




Useful words and observations

axis -pl. axes focus - pl. focuses or foci

locus -pl. loci vertex -pl vertexes or vertices

ellipse

hyperbola -pl hyperbolas or hyperbole




Saying math 5 - Geometry

angles

circles, semicircles, circumferences




triangles

polygons




Useful words and observations

annulus -pl. annuli or annuluses

rhombus -pl. rhombuses or rhombi trapezium -pl. trapeziums or trapezia

Saying math 6 - Miscellanea

Lines:

• : full / solid

• : dotted

• : dash-dot

• : dash and dash / broken

Taken from: http://www batmath it/eng/say/say htm17

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