_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***, **
**A****B, **
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**,**

O5 The Rules of Sign in Addition and Multiplication**,**

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

reductio ad absurdum**,**

rational numbers**,**

rules of sign in addition and multiplication**,**

s

sequences (finite and infinite)**, **

sets (1st reading)**, **

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