## topic index

_a_,_b_,_c_,_d_,_e_,_f_,_g_,_h_,_i_,_j_,_k_,_l_,_m_,_n_,_o_,_p_,_q_, _r_,_s_,_t_,_u_,_v_,_w_,_x_,_y_,_z_

symbols
,   ,   ,   ,   ,   XY,   f:XY,   XY,   g f,   AB,   as material implication,   ,   ,   ε-neighborhoods,
{ }: the set consisting of what is between the curly braces
: for every or for all (which also means for any)
: there exists
: such that

a
absolute value of a real number,
absolute value property 1   |a|0 ,
absolute value property 2   |ab| = |a|·|b| ,
absolute value property 3   |a|²=a² ,
absolute value property 4   |a+b||a|+|b|,
absolute value property 5   |a-b|||a|-|b||,
addition as a postulated function in the real number system,
argument of a function,
associativity,

b
being in a set,
bounded from above,
bounded from below,

c
commutativity,
complement of a set,
composition of functions,
cartesian product,

d
decimals,
definition of division,
definition of subtraction,
difference of sets,
distributivity,

e
elements of a set,
empty set,
ε(epsilon)-neighborhoods,
equality of sets,
equality of sets in terms of subsets,
existence of neutral elements,
existence of inverses for addition and multiplication,

f
F1   ommission of parentheses in sums and products,
F2   irrelevance of order in sums and products,
uniqueness of sums and products   (general argument for F1 and F2),
F3   (unique solution to   x+a=b),
F4   (unique solution to   x·a=b),
F5   (zero times any number is zero),
F6   -(-a) = a,
F7   (a)= a,
F8   -(a+b) = (-a)+(-b),
F9   ( a · b )  =  a· b,
F10   -a = (-1) · a,
field of two elements,
finite set,
fractions,
function from X to Y (description),
function from X to Y (definition),
function (general definition),

g
greatest lower bound,
greatest lower bound (property),
greater than symbol,

h
i
identity function,
if A then B (as material implication),
if and only if (as a double arrow),
if and only if (its two parts),
the image of a set under a function,
indexing families of sets,
inf (infimum),
infinite set,
integers,
intersection of sets,
intersection of complements equals complement of union,
inverse functions,
the inverse image of a set under a function,

j
k
l
l.u.b. (least upper bound),
least upper bound,
least upper bound (any real number less than the least upper bound of a set is less than some element of the set),
least upper bound (uniqueness),
least upper bound (PROPERTY),
less than symbol,
LUB1, The Archimedean Principle
LUB2, Arbitrarily small positive rational numbers
LUB3, Nearest integers to any real number
LUB4, Rationals with a given denominator near a given real
LUB5, Arbitrarily accurate approximation of reals by rationals

m
material implication (under SYMBOLIC LOGIC),
max S,
min S,
multiplication as a postulated function in the real number system,

n
the natural numbers,

o
O1   Trichotomy   ab,   a=b,   or   ab,
O2   Transitivity   ab   and   bc   imply that   ac,
O3   The sum of the greaters is greater,
O4   The product of the greater positives is greater,
O6   The squares of the real numbers are greater than or equal to zero,
O7   The multiplicative inverses of the positive real numbers are greater than zero,
O8   The multiplicative inverse of the positive greater is less,
O9   The rules of arithmetic,
one is greater than zero,
one-one functions,
onto functions,
one-one onto functions,
Order Property (The),
ordered pairs,

p
problem 5 chapter 1,

q
r
rational numbers,

s
sequences (finite and infinite),
subsets,
subset symbols - reading of,
subtraction (definition),
sup (supremum),
symbolic logic,

t
Transitivity   ab   and   bc   imply that   ac,
the triangle inequality   |a+b||a|+|b|,
the generalized triangle inequality   |a + a + ··· + a| |a| + |a| + ··· + |a|,
Trichotomy   ab,   a=b,   or   ab,

u
union of sets,
upper bound,
upper bound on the empty set,

v
w
x
y
z