# A Gentle Intro duction to TEX - Doob M.

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Miscellaneous symbols

\aleph I \ell 3? \Ee \Im

d \partial OO \infty Il \l Z \angle

V \nabla \ \backslash V \forall 3 \exists

—I \neg b \f Iat tt \sharp \natural

d> Exercise 5.10 Typeset: (Vx ª 3?) (3ó ª SR) ó > x.

5.2 Fractions

There are two methods of typesetting a fraction: it can be typeset either in the form 1/2 or in the form The first case is just entered with no special control sequences, that is, $1/2$. The second case uses the control word \over and the following pattern:

{enumerator> \over <denominator>}. Hence$${a+b \over c+d}.$$ gives òùõüîîê: 139-140

a + b c + d'

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A T^X intro (Canadian spelling) Section 5: No math anxiety here!

D> Exercise 5.11 Typeset the following: ^ à+ü+å Ô a + I + c'

d> Exercise 5.12 Typeset: What are the points where f(x,y) = ù/(õ,ó) = 0?

5.3 Subscripts and superscripts

Subscripts and superscripts are particularly easy to enter using T^jX. The characters _ and ~ are used to indicate that the next character is a subscript or a superscript. Thus $x~2$ gives X2 and $x_2$ gives x^- To get several characters as a subscript or superscript, they are grouped together within braces. Hence we can use $x~{21}$ to get x21 and $x_{21}$ to get X21- Notice that the superscripts and subscripts are automatically typeset in a smaller type size. The situation is only slightly more complicated for a second layer of subscripts or superscripts. You can not use $x_2_3$ since this could have two possible interpretations, namely, $x_{2_3}$ or ${x_2}_3$; this gives two different results: 0? and X23, the first of which is the usual mathematical subscript notation. Thus you must put in the complete braces to describe multiple layers of subscripts and superscripts. They may be done to any

IeveL rIfeXbook: 128-130

To use both subscripts and superscripts on one symbol, you use both the _ and ~ in either order. Thus either $x_2~l$ or $x~l_2$ will give x\.

D> Exercise 5.13 Typeset each of the following: ex (Ãõ åã7! + I = 0 Xq Xq2 2õ .

D> Exercise 5.14 Typeset: V2f(x,y) = +

A similar method is used for summations and integrals. The input of $\sum_{k=l}~n k~2$ will give YZ=i anfI $\int_0~x f (t) dt$ will give J1f(t)dt. òùõüîîê: 144-145

Another use of this type of input is for expressions involving limits. You can use $\lim_{n\to \infty}({n+1 \over n})~n = e$ to get Iimn^00= e.

D> Exercise 5.15 Typeset the following expression: 1³òõ_þ(1 + x) i = e.

d> Exercise 5.16 Typeset: The cardinality of (^00,00) is Ni.

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À ÒöÕ intro (Canadian spelling)

Section 5: No math anxiety here!

Exercise 5.17 Typeset: limx_>0+ Xõ = I.

Here’s a hint to make integrals look a little nicer: look at the difference between Jq f(t)dt and Jg f(t) dt. In the second case there is a little extra space after f(t), and it looks nicer; \, was used to add the additional space.

Exercise 5.18 Typeset the following integral: Jq1 Çæ2 dx = I.

5.4 Roots, square and otherwise

To typeset a square root it is only necessary to use the construction \sqrt{...}. Hence $\sqrt{x~2+y~2}$ will give \Jx? + y2. Notice that T^X takes care of the placement of symbols and the height and length of the radical. To make cube or other roots, the control words \root and \of are used. Youget \/l + xn from the input $\root n \of {l+x~n}$. òùõüîîê: ³çî-³ç³

A possible alternative is to use the control word \surd; the input $\surd 2$ will produce ë/2.

Exercise 5.19 Typeset the following: \/2 \/¯0 B^x.

ó % ó

Exercise 5.20 Typeset: ||æ|| = s/x • x.

Exercise 5.21 Typeset: ô(³) = -^== f* e x^l2 dx

5.5 Lines, above and below

Use the constructions \overline{.. J and \underline{.. J to put lines above or below mathematical expressions. Hence $\overline{x+y}=\overline x + \overline y$ gives x + ó = X + ó. But notice that the lines over the letters are at different heights, and so some care is necessary. The use of \overline{\strut x} will raise the height of the line over x.

ÒÙÕÜîîê: 130-131

To underline non-mathematical text, use \underbar{...}.

39

A T^X intro (Canadian spelling) Section 5: No math anxiety here!

D> Exercise 5.22 Typeset the following: x ó x + ó.

5.6 Delimiters large and small

The most commonly used mathematical delimiters are brackets, braces, and parentheses. As we have seen, they may be produced by using [ ] \{ \} ( ) to get []{}()•

Sometimes larger delimiters increase the clarity of mathematical expressions, as in

(a x (b + c)) ((a x b) + c).

To make larger left delimiters the control words \bigl, \Bigl, \biggl, and \Biggl are used

in front of the delimiter; similarly, \bigr, \Bigr, \biggr, and \Biggr are used for the right òùõüîîê: 145-147

delimiters. Hence $\Bigl [$ and $\Bigr] $ will produce and j.

Here is a table to compare the size of some of the delimiters.

Delimiters of various sizes

\{ } \> ( ( ) )

\bigl\{ } \bigr\} ( YbigK ) \bigr)

\Bigl\{ j \Bigr\} ( \Bigl( j \Bigr)

\biggl\{ j \biggr\} ^ YbiggK ^ \biggr)

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