About TonesInDeepFreeze

About Some of the symbols I use:

~ ... it is not the case that

-> ... implies

<-> ... if and only if

& ... and

v ... or

A ... for all

E ... there exists a/an

E! ... there exists a unique

Axy ... for all x and for all y [for example]

Exy ... there exists an x and there exists a y [for example]

=> ... implies [in the meta-language]

<=> ... if and only if [in the meta-language]

if P(x) is a formula, then, in context, P(y) is the result of replacing all free occurrences of x with y [for example]

= ... equals

not= ... does not equal

< ... is less than

<= ... is less than or equal to

> ... is greater than

>= ... is greater than or equal to

+ ... plus

- ... minus

* ... times

/ ... divided by

^ ... raised to the power of

! ... factorial

e ... is an element of

0 ... the empty set (also, zero)

w ... the set of natural numbers [read as 'omega']

N ... the set of natural numbers

Q ... the set of rational numbers

R ... the set of real numbers

{x | P} ... the set of x such that P [for example]

{x y z} ... the set whose members are x, y and z [for example]

<x y> ... the ordered pair such that x is the first coordinate and y is the second coordinate [for example]

(x y) ... the open interval between x and y [for example]

(x y] ... the interval between x and y, including y, not including x [for example]

[x y) ... the interval between x and y, including x, not including y [for example]

[x y] ... the closed interval between x and y [for example]

| | ... the absolute value of

U ... the union of

P ... the power set of

/\ ... the intersection of

x u y ... the union of x and y [for example]

x n y ... the intersection of x and y [for example]

x\y ... x without the members of y [for example]

c ... the set complement of

1-1 ... bijection

|- ... proves

|/- ... does not prove

|= ... entails

|/= ... does not entail

PA ... first order Peano arithmetic

S ... the successor of

# ... the Godel number of

card ... the cardinality of

Z ... Zermelo set theory

ZC ... Zermelo set theory with the axiom of choice

ZF ... Zermelo-Fraenkel set theory

ZFC ... Zermelo Fraenkel set theory with the axiom choice

Z\I ... Zermelo set theory without the axiom of infinity

(Z\I)+~I ... Zermelo set theory with the axiom of infinity replaced by the negation of the axiom of infinity

Z\R ... Zermelo set theory without the axiom of regularity

ZF\R ... Zermelo-Fraenkel set theory without the axiom of regularity

ZFC\R ... Zermelo Fraenkel set theory with the axiom choice without the axiom of regularity

p ... possibly

n ... necessarily

when needed for clarity, ' ' or " " indicate an expression not its referent ('Sue' is a name, Sue a person)
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Favourite philosophers Alonzo Church, Steven Wright, Sonny Clark
Favourite quotations "Are you chewing gum?"
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TonesInDeepFreeze

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