# Symbols:Abbreviations

## A

### AC

The axiom of choice.

Same as AoC.

### ACC

The ascending chain condition.

### AoC

The axiom of choice.

Same as AC.

## B

### BNF

Backus-Naur Form (previously Backus Normal Form until the syntax was simplified by Peter Naur).

It was Donald Knuth who suggested the name change, on the grounds that "normal" is an inaccurate description.

### BPI

The Boolean Prime Ideal Theorem.

## C

### CNF

Conjunctive normal form.

## D

### DCC

Descending chain condition

### DNF

Disjunctive normal form.

## E

### EE

Context: Predicate Logic.

Rule of Existential Elimination, which is another term for the Rule of Existential Instantiation (EI).

### EG

Context: Predicate Logic.

Rule of Existential Generalisation.

### EI

Context: Predicate Logic.

Rule of Existential Instantiation.

Alternatively, Rule of Existential Introduction, which is another term for the Rule of Existential Generalisation (EG). Beware.

### EMF

Context: Electromagnetic theory.

Electromotive force.

## F

### FCF

Finite continued fraction.

## G

### GCD or g.c.d.

Greatest common divisor. Also known as highest common factor (h.c.f.).

## H

### HCF or h.c.f.

Highest common factor. Also known as greatest common divisor (g.c.d.).

## I

If and only if.

### ICF

Infinite continued fraction.

### I.V.P.

$(1): \quad$ The intermediate value property.
$(2): \quad$ An initial value problem.

## L

### LCM, lcm or l.c.m.

The lowest (or least) common multiple.

### LHS

Left hand side.

In an equation:

$\textrm {Expression}\ 1 = \textrm {Expression}\ 2$

the term $\textrm {Expression}\ 1$ is the left hand side.

This is often abbreviated to LHS.

### LSC

Lower semicontinuous.

## N

### NNF

Negation normal form.

## O

### ODE

Ordinary differential equation.

## P

### PCI

Principle of Complete Induction (or Principle of Complete Finite Induction).

### PCFI

Principle of Complete Finite Induction.

### PDE

Partial differential equation.

### PFI

Principle of Finite Induction.

### PGF or p.g.f.

Probability generating function.

### PMF or p.m.f.

Probability mass function.

### PMI

Principle of Mathematical Induction.

### PNT

Prime Number Theorem.

## Q

### Q.E.D.

Quod Erat Demonstrandum

## R

### RHS

Right hand side.

In an equation:

$\textrm {Expression}\ 1 = \textrm {Expression}\ 2$

the term $\textrm {Expression}\ 2$ is the right hand side.

This is often abbreviated to RHS.

## S

### SCF

Simple continued fraction.

### SFCF

Simple finite continued fraction.

### SHM

Simple harmonic motion.

### SICF

Simple infinite continued fraction.

### SUVAT

A category of problems in elementary applied mathematics and Newtonian physics involving a body $B$ under constant acceleration $\mathbf a$.
They consist of applications of the equations:

### $(1):$ Velocity after Time

$\mathbf v = \mathbf u + \mathbf a t$

### $(2):$ Distance after Time

$\mathbf s = \mathbf u t + \dfrac {\mathbf a t^2} 2$

### $(3):$ Velocity after Distance

$\mathbf v \cdot \mathbf v = \mathbf u \cdot \mathbf u + 2 \mathbf a \cdot \mathbf s$

where:

$\mathbf u$ is the velocity at time $t = 0$
$\mathbf v$ is the velocity at time $t$
$\mathbf s$ is the displacement of $B$ from its initial position at time $t$
$\cdot$ denotes the scalar product.

The term SUVAT arises from the symbols used, $\mathbf s$, $\mathbf u$, $\mathbf v$, $\mathbf a$ and $t$.

## U

### UF

Ultrafilter Lemma.

### UFD

Unique factorization domain.

### UL

Ultrafilter Lemma.

### URM

Unlimited register machine: an abstraction of a computing device with certain particular characteristics.

## W

### WFF

Well-formed formula.

### WLOG

Without loss of generality.

Suppose there are several cases which need to be investigated.

If the same argument can be used to dispose of two or more of these cases, then it is acceptable in a proof to pick just one of these cases, and announce this fact with the words: Without loss of generality, ..., or just WLOG.

### WRT

(Differentiation) with respect to.

When performing calculus operations, that is differentiation or integration, one needs to announce which variable one is "working with".

Thus the phrase with respect to is (implicitly or explicitly) part of every statement in calculus.

The abbreviation WRT or w.r.t. is frequently seen, and often pronounced something like wurt.

## Z

### ZF

Zermelo-Fraenkel set theory.

### ZFC

Zermelo-Fraenkel set theory with the Axiom of Choice.