abstractmath.org 2.0

help with abstract math

Produced by Charles Wells Revised 2016-06-07
Introduction to this website website TOC blog

# INDEX TO THE ABSTRACTMATH WEBSITE

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#### A

a, an

abstract math

abstract
object

abstraction

abuse of notation

accented characters

add, addition

after (in discourse)

aleph

algebra

algorithm

alias

alibi

all

alphabets

always

ambient

analogy

and

(conjunction)

(English word)

__ angle
bracket __

__anonymous notation__

__ antecedent __

antisymmetric

any

approximation (of real numbers)

arbitrary

argument

arrow
notation

article

(definite)

(indefinite)

assertion

(symbolic)

assume

assumption

asterisk

axiomatic method

####

#### B

baby example

bar

(accent)

(notation for decimals)

bare
delimiters

barred arrow notation

base (of a logarithm)

be

before (in discourse)

behaviors

binary operation

blackboard
bold

boldface

bound variable

boundary value (of a function)

braces

bracket

but

####

#### C

calculate

call

canonical structure

caron

case

--(of letters)

proof by --

category (two
meanings)

character (two
meanings)

check (accent)

chunking

circumflex

closedunder

closure properties

of the natural numbers

of the integers

of the rational numbers

codomain

cognitive dissonance

cograph

co-intimidator

colon
equals

combination

comma

comprehension, method of

conceptual

conclusion

conditional assertion

conjunction

consequent

constraint

constructor

contain

context

contradiction

contrapositive

-- method

convention

converse

coordinatewise

counterexample

corollary

covert
curriculum

crisp

curly
bracket

cycle notation

####

#### D

decreasing

default

define

definiendum

defining condition (in setbuilder notation)

defining phrase (of a definition)

definite article

definite description

definition

degenerate

delimiter

DeMorgan laws

denote

density

of the rational numbers

of the real numbers

dependent
variable

dependency
relation

derivative

description

devious definition

direct
method

discontinuous function

disjoint

disjunction

distinct

division

doing math

domain

-- of
a function

(two
meanings)

dysfunctional behaviors

####

####

#### E

each

e.g.

-- element notation

-- element symbol

empty set

-- symbol

encapsulate

endograph

enthymeme

equals

--symbol

equation

equipped

equivalance (of assertions)

equivalent

establish notation

evaluate

every

exact number

exactly when

examples

exhaustion (proof by)

existence statement

existential bigamy

existential quantifier

expansive generalization

extension (of an
assertion)

####

#### F

fallacy

family (two
meanings)

fencepost error

field

find

fix

follow

following are equivalent

form of proof

formula

(for a function)

(two meanings)

forward reference

foundations of math

fraktur

free variable

function

function on its index set

functional property

fuzzy

####

#### G

generalization

give

glossary

glue

graph

--
of a function

(two
meanings)

grasshopper

Greek
alphabet

group

guessing

####

#### H

hÃ¡ček

hat

hypothesis

####

#### I

I (two meanings)

identify

identity

(two meanings)

-- function

i.e.

if

(usage)

(conditional)

if and only if

image (mental representation)

implication

imply

in

in general

include

inclusive or

inclusion

increasing

indefinite article

indefinite description

independent variable

index set

inequality

inert

infix notation

inhabit

injective

input

integer

integral

intent of assertion

interval

intuition

italic

#### J

jump
the fence

just

just in case

juxtaposition

####

#### K

kind

####

#### L

large

law

large

tm#lemma">lemma
let

lg

linear

links to math sites

list notation (for sets)

literalism

ln

logarithm

logic

logical construction

look ahead

lower-case
letter

lowest terms

#### M

macron

malrule

map, mapping

mathematical
logic

mathematical object

__ mathematical structure __

maximize

mean

mental representation

metaphor

method addiction Â

method of deduction

minimize

minus

mod

model

modulo

modus
ponens

multiplication symbol

multivalued
function

must

####

#### N

name

namely

narrative proof

natural number

nearness

necessary

negation

negative

nonincreasing

nondecreasing

nonnegative

notation

number theory

#### O

obvious

one
to one

only if

onto

operator

opposite (of a
relation)

or

order

(two
meanings)

ordered pair

outfix notation

output

overloaded

####

#### P

pairwise
disjoint

parameter

parentheses

parenthetic assertion

partial
function

partition

(different meanings)

-- of a set

pattern recognition

permutation

(two meanings)

Perrin function

physical representation

plus

pointy
brackets

Polish notation

polymorphic

pons asinorum

positive

(two meanings)

postcondition

postfix notation

power

powerset

precisely when

precondition

prefix notation

prime

process

product

product rule

proof

-- by contradiction

-- by example

narrative --

structure
of --

proper

property

proposition

purple prose

#### Q

quadratic formula

quantifier

logical operation

symbol

quantity

####

#### R

r.a.a.

rabbit out of a hat

range

(two
meanings)

ratchet effect

ratio

rational number

real line

real number

real variable

recall

reconstructive generalization

redundancy

reflexive

relation

representation

of functions

of natural numbers

of the rational numbers

of
the real numbers

result

reverse Polish notation

revise

rewrite according to the definition

rich
view

rigorous view

ring
with identity

root

rule

####

#### S

said to be

scope

self-monitoring

semantic contamination

sequence

set

equality of _

definition of _

specification
for _

setbuilder notation

sign

sine-blur function

singleton set

slash

some

specification

split definition

square
brackets

standardization
in math

statement

stronger (for
conditional statements)

structure-preserving function

structure

style (of typeface)

subexpression

subset

subscript

substitution

subtract

meaning

usage

such that

sufficient

sum

suppose

suppression of parameters

surjective

symbol

symbol manipulation

symbolic
assertion

symbolic
expression

symbolic term

symbolic
logic

symbolic statement

symmetry

synecdoche

#### T

table (to define a function)

tangent

term

part of a sum

multiple meanings

TFAE

the

then

there is

theorem

theory of functions

tilde

transformation, transformer

translation problem

trial
and error

trigonometric functions

trivial

truth set

truth table

truth value

tuple

twiddle

two

two-column format

two-line notation

type

_labeling

typical

#### U

under

underlying set

understanding math

unique

--
misuse of

uniqueness

unit

unit
circle

unit
interval

unity

universal

generalization

instantiation

quantifier

universally true

assertion

conditional

unknown

unnecessarily weak assertion

unwind

unpack

up to

upper-case letter

useful
behaviors

#### V

vacuously
true

value (of a function)

variable

variable object

variations in meaning

Venn diagram

#### W

walking blindfolded

well-defined

when

when and only when

whenever

where

without loss of generality (WLOG)

witness

word-length
function

####

#### X

#### Y

####

#### Z

zero

zooming

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