# Symbols:Abbreviations

## Contents

## A

### AC

- The axiom of choice.

Same as AoC.

### ACC

### 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

## C

### CNF

## D

### DCC

### DNF

## E

### EE

Context: Predicate Logic.

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

### EG

Context: Predicate Logic.

### EI

Context: Predicate Logic.

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

### EMF

Context: Electromagnetic theory.

## F

### FCF

## 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

### iff

### ICF

### I.V.P.

- $(1): \quad$ The intermediate value property.

- $(2): \quad$ An initial value problem.

## J

## K

## L

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

### 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

## M

## N

### NNF

## O

### ODE

## P

### PCI

### PCFI

### PDE

### PFI

### PGF or p.g.f.

### PMF or p.m.f.

### PMI

### PNT

## Q

### Q.E.D.

## 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

### SFCF

### SHM

### SICF

### 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 $t$.

## T

## U

### UF

### UFD

### UL

### URM

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

## V

## W

### WFF

### WLOG

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

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**.

## X

## Y

## Z

### ZF

### ZFC

- Zermelo-Fraenkel set theory with the Axiom of Choice.