# Symbols:Abbreviations

## Contents

## A

### AC

- The axiom of choice.

Same as AoC.

### ACC

### acos

- Abbreviation for
**arccosine**.

### acosec

- Abbreviation for
**arccosecant**.

### acosech

- Abbreviation for
**arc-cosech**.

### acosh

- Abbreviation for
**arc-cosh**.

### acot

- Abbreviation for
**arccotangent**.

### acoth

- Abbreviation for
**arc-coth**.

### acsc

- Abbreviation for
**arccosecant**.

### acsch

- Abbreviation for
**arc-cosech**.

### actn

- Abbreviation for
**arccotangent**.

### actnh

- Abbreviation for
**arc-coth**.

### adj

### a.e.

- Abbreviation for
**almost everywhere**.

### agm

- Abbreviation for
**arithmetic-geometric mean.**

### alg.

### aln

- Abbreviation for the
**antilogarithm**of the**natural logarithm**.

### alog

- Abbreviation for the
**antilogarithm**of a**general logarithm**.

- If no base is given, the
**common logarithm**(that is, base $10$) is assumed.

### amp

- Abbreviation for
**amplitude**.

### AoC

- The axiom of choice.

Same as AC.

### arg

- Abbreviation for
**argument (of complex number)**.

## 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

### c.d.f.

### ch

- Abbreviation for
**hyperbolic cosine**.

### ch${}^{-1}$

- Abbreviation for
**inverse hyperbolic cosine $\cosh^{-1}$**.

### 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.

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

## H

### HCF or h.c.f.

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

## I

### iff

### ICF

### I.V.P.

#### I.V.P.: 1

#### I.V.P.: 2

## 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**.

### 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**.

## 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

- Ultrafilter Lemma (also UL).

### UFD

### UL

- Ultrafilter Lemma (also UF).

### 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 or w.r.t.

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.

## X

## Y

## Z

### ZF

### ZFC

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