TonesInDeepFreeze
Bio
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)
~ ... 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)
Favourite Philosopher
Alonzo Church, Steven Wright, Sonny Clark
Favourite Quotations
"Are you chewing gum?"
Comments