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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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