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Mathematical English (a brief summary) Jan Nekovár Université Paris 6 Capital Greek letters used in mathematics B Beta Γ Gamma ∆ Delta Θ Theta Λ

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Mathematical English (a brief summary)

Jan Nekov´ar

Universit´e Paris 6c

?Jan Nekov´ar 2011 1

Arithmetic

Integers

0zero10ten20twenty

1one11eleven30thirty

2two12twelve40forty

3three13thirteen50fifty

4four14fourteen60sixty

5five15fifteen70seventy

6six16sixteen80eighty

7seven17seventeen90ninety

8eight18eighteen100one hundred

9nine19nineteen1000one thousand

-245minus two hundred and forty-five

22 731twenty-two thousand seven hundred and thirty-one

1 000 000one million

56 000 000fifty-six million

1 000 000 000one billion [US usage, now universal]

7 000 000 000seven billion [US usage, now universal]

1 000 000 000 000one trillion [US usage, now universal]

3 000 000 000 000three trillion [US usage, now universal]

Fractions [= Rational Numbers]

12 one half38 three eighths 13 one third269 twenty-six ninths 14 one quarter [= one fourth]-534 minus five thirty-fourths 15 one fifth237 two and three sevenths 117
minus one seventeenth

Real Numbers

-0.067minus nought point zero six seven

81.59eighty-one point five nine

-2.3·106minus two point three times ten to the six [=-2 300 000minus two million three hundred thousand]

4·10-3four times ten to the minus three

[= 0.004 = 4/1000four thousandths]

π[= 3.14159...]pi [pronounced as 'pie"]

e[= 2.71828...]e [base of the natural logarithm] 2

Complex Numbers

ii

3 + 4ithree plus four i

1-2ione minus two i1-2i= 1 + 2ithe complex conjugate of one minus two i equals one plus two i

The real part and the imaginary part of 3 + 4iare equal, respectively, to 3 and 4.

Basic arithmetic operations

Addition:3 + 5 = 8three plus five equals [= is equal to] eight Subtraction:3-5 =-2three minus five equals [=...] minus two Multiplication:3·5 = 15three times five equals [=...] fifteen Division:3/5 = 0.6three divided by five equals [=...] zero point six (2-3)·6 + 1 =-5two minus three in brackets times six plus one equals minus five

1-32+4

=-1/3one minus three over two plus four equals minus one third

4! [= 1·2·3·4]four factorial

Exponentiation, Roots

5

2[= 5·5 = 25]five squared

5

3[= 5·5·5 = 125]five cubed

5

4[= 5·5·5·5 = 625]five to the (power of) four

5 -1[= 1/5 = 0.2]five to the minus one 5 -2[= 1/52= 0.04]five to the minus two⎷3 [= 1.73205...]the square root of three

3⎷64 [= 4]the cube root of sixty four

5⎷32 [= 2]the fifth root of thirty two

In the complex domain the notation

n⎷ais ambiguous, since any non-zero complex number hasndifferentn-th roots. For example,4⎷-4 has four possible values:±1±i(with allquotesdbs_dbs2.pdfusesText_2