Saying MathsVersiWords

Saying math - Foreword General remarks •

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Individual mathematicians often have their own way of pronouncing mathematical expressions 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 different mathematical 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 and length of pauses. The previous example can be read as "the "the square root of a -pause- all plus b" b" (longer expression) or "the "the square root of a -pause- plus b", b", for the first expression, and "a+b "a+b all under the square root " or "the "the square root of b", for the second expression. Observe the shifting of the -pause-. -pause- a plus b",

Directions •

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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, Edition, and the English equivalent. The pronunciation is written using the International the International Phonetic Alphabet (IPA). Alphabet (IPA). We have added a column with the key used on PC keyboards under Windows Operating System (Symbol font) to obtain the letter.

Ν

Capital

Lowcase

English name

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( )

th theta

th

Q , q (J)

Ι

ι

iota

i

I,i

Κ

κ

kappa

k

K,k

Λ

λ

lambda

l

L,l

Μ

μ

mu

m

M,m

ν

Pronunciation

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

ρ

rho (-pl. rhos)

r

R,r

Σ

σς

sigma

s

S , s (V)

Τ

τ

tau

t

T,t

Υ

υ

upsilon

u

U,u

phi (-pl. phis)

ph

Φ

(φ)

F , f (j)

Χ

χ

chi

ch - kh

C,c

Ψ

ψ

ps p si

ps

Y,y

Ω

ω

omega

o

W,w

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

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Saying math 2 - Mainly numbers Numbe rs: general gen eral remarks re marks | 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, tenths, but one hundred point five is by far more common; 239.36 is two hundred thirty-nine and thirty-six hundredths, hundredths, but two hundred thirty-nine point three six is by far more common; in British English we use and when and when saying numbers in the hundreds: o 105 is one hundred and five; five; o in American English we do not use and when and when saying numbers in the hundreds: 105 is one hundred five; five; o anyhow we have also found on the Internet something like this: 105 is hundred five; five; so, as what is "correct" changes with time, choose your standard and o follow it! The "0" (oh, nought, zero, zero, love, nil) oh o after the decimal point: 27.05 is twenty-seven point oh five; five; in years: 1907 is nineteen oh seven; 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 is zero;; before a decimal point, mainly in American English, but also in British English: 0.05 is zero is zero point oh five, five, instead of the more "traditional" form "nought point oh five"; for the temperature: -7°C is seven is seven degrees below zero, zero, which you can also say minus seven; seven; nil o in football scores: "Italy wins 3-0" is "Italy wins three nil " (also three to nil ); ); sometimes nothing is nothing is used in the place of nil of nil "3-0" can be three to nothing ; o love in tennis games: "the score of the game is 15-0" is "the score of the game is fifteen is fifteen love"; love"; "0-0" is love all or all or love love game. game.

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The decimal point o the numbers after the decimal point are all read separately 0.0023 is nought point oh oh two three; 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; five; o in periodic numbers we use "recurring": 5.376666... is five is five point three seven -pause- six recurring , while 5.376376376... is five 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 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; cents; 47.99s (seconds) is forty is forty seven seconds ninety-nine hundredths; hundredths; 3.87m (meters) is three meters eighty-seven centimetres. Kinds of numbers natural, whole, integer, rational, irrational, real, complex o (imaginary) o odd, even fractional o o prime o binary, octal, decimal, hexadecimal random o 

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

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

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

x≤a≤y

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).


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a+b=s (addition)

a and b are the addends, addends, s is the sum the sum,, a and b are also the items of the addition. a plus b is ( to) s / equals / is equal to)

a+b=s a-b=d (subtraction or difference)

a and b is ( / equals / is equal to) s s is the sum of a and b a is the minuend , b is the subtrahend the subtrahend , d is the remainder or remainder or the difference a minus b is ( / equals / is equal to) d

a-b=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 the factors or the multipliers, multipliers, p is the product the product a times b is ( / equals / is equal to) p

a×b=p, or a·b=p, or simply ab=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 = a is the dividend , b is the divisor , q is the quotient or quotient or the ratio q (division) 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 operations

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

(fraction)

a is the numerator , b is the denominator (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 or a over b. b. Cardinal numbers for the numerator and ordinal numbers for the denominator are also used (as in Italian): Special cases are

(a/one half ), ),

is a third ,

(a/one quarter ), ),

is two thirds. thirds. (three halves), halves),

(three quarters), quarters), and similar. The special notation sometimes used for improper fractions, as


, is said three and a half .

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Numbers: advanced calculations |x| or abs(x)

The absolute value of x

a b

a is the base, 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 x nth root x / nth root of x nth root -pause- x cubed or cubed or nth 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 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) n

a1 × 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


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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 squared (but probably nobody will understand what you mean if he can't read the blackboard or the transparency!!) parenthesis -pl. parentheses -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

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Saying math 3 - Logic and Sets, Functions Logic and sets there exists !

there exists only one

p

non p / not p

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such that (in 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 A

U

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)= (A)= {0,1}A

the 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


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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, domain, T the range (rarely the codomain) 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 place of image - we do not agree with with this)

f -1(B)

the inverse image of B / the pre-image of B

f:x x

y y

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

f(x)

f x / f of x / the function f of x

f -1(x)

f inverse

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 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

-pause-

of 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


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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 x 1

the second partial derivative of f with respect to x1 surjection / surjective map / onto map Terms about functions

injection / injective map bijection / bijective map / one-to-one map composition map piecewise defined map


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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

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Useful words and observations


axis -pl. axes focus - pl. focuses pl. focuses or foci foci locus -pl. loci vertex -pl vertexes or vertices ellipse hyperbola -pl hyperbolas or hyperbole or hyperbole

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Saying math 5 - Geometry angles

circles, semicircles, circumferences


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triangles

polygons


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Useful words and observations

annulus -pl. annuli or annuluses or annuluses rhombus -pl. rhombuses or rhombi or rhombi trapezium -pl. trapeziums or trapezia or trapezia

Saying math 6 - Miscellanea Lines: • • •

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: full / / solid : dotted : dash-dot : dash and dash / broken


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Saying MathsVersiWords

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