Examples... of the Simplified

Notation of Mathematical

Formulae

3,1 ab аЪ\с or abc 1

[a line must neither c

begin nor end with

the solidus]

3,2 CL±1 + d {a + b)\c + d or (a + b) c"1 + d

3,3 —^— aj{b + e) ór a(b + c)_1

/) -I с

3,4 í±± (a + b)l(c-d) or (a + b){c-dyl

с — d

- c a + b (a + b)jc + x

3,5 ----------h x------------------

_C______ b - У

• b-y

36 «J^ [(e + b)/(z + x)]:(i + y)

3,7

3,8

Z + X

b + у

e2 г

eia+*b or eila+b)

Nt

Nt ,N2

Q + v

Q + v Q

N2

Q

128

4 BRACKETS

33

There are six types of brackets: () parentheses, [] brackets, { } braces, | | vertical rules,

] double brackets, and < > angular brackets. The last three types are applied for special

purposes; vertical rules enclose absolute values and angular brackets, even when not

used in pairs, mark closed intervals, e.g. < ), ( > (In England, reversed parentheses are

sometimes used for this function, the reversion taking place at the open end of the

interval — ((, )), ) ( ). They can also be applied as brackets of the "first degree" within

the sequence {[( )]} which has been established as a standard convention in this country.

Double brackets, owing to their conspicuousness, can be successfully used for bracketing

analogical expressions at both sides of one equation or in a system of equations. An¬

gular and double brackets can be used to advantage by the author when correcting the

proofs, if he discovers, for example, that it is necessary to bracket within the sequence

of brackets some other expression whose involution was erroneously omitted. He does

not therefore need to rewrite all the brackets of the higher order.

The mathematical printer should have all the above-mentioned types of brackets at his

disposal with type faces of 12, 26, 38 and 50 points. For the rules, it will, of course, be

sufficient to be cut to appropriate lengths.

Brackets of a deeper body must be fitted together by hand. If, however, the author uses

the typographically simplified notation (see Sect. 3.), it will hardly ever be necessary to

take this step.

The usual order of brackets {[( )]} is not absolutely obligatory for the author. The printer

must not cling to their stereotyped application and order. In various fields of mathematics

it is customary to use certain types of brackets; thus e.g. the "higher" brackets in the

sequence are turned into "lower" ones, or square brackets are applied to emphasize

analogical, homogeneous expressions, even if, from the standpoint of the sequence, this

is not necessary in the particular case in the context, since the expression does not

contain parentheses:

{G'ilbí и G'itb2 и ...} , {aiß'ti и a2G'u и...}.- G'lt,

wi,x = к2 —, wa,x - blk0a2 Ci (cosh-----1 ) + C2 sinh - ,

b20 LI«/ «J

Tl,x — K2

'2 Г

a т0іХ - b\k0a

'o L

Ct sinh —HC, cosh -

;]

Щх)ах, №bx...dx

129