., Set-Fmla vs.
"Andy was very close to winning the second set.
(See Set theory: Axiomatic set theory.)
Cook again, until the omelette has set further, then push those set parts into the centre of the omelette again.
For example, any set is a subset of itself, and Ø is a subset of any set.
Early set theorists and an array contemporary metaphysicians reject the empty set.
Now suppose that the set-theoretical universe forms a set: the set of all sets.
Unlike a finite set, an infinite set can have the same cardinality as a proper subset of itself.
A set of reals is said to have the perfect set property iff it is either countable or contains a perfect subset.
The axioms of set theory imply the existence of a set-theoretic universe so rich that all mathematical objects can be construed as sets.
By such a system we mean a set X which we think of as variables (any set will do), and then a function e from X to its power set ℘X.
The study of alternative set theories can dispel a facile identification of “set theory” with “Zermelo-Fraenkel set theory”; they are not the same thing.
If the specified set is a set actually believed, or even a set which would be believed by people like us at some limit of inquiry, coherentism involves the rejection of realism about truth.
From Cameron Winklevoss, set theorists can derive the set containing him, then the set containing that set, then the set containing that larger set, and so on.
Rathjen (2012b) shows that CZF augmented by the power set axiom exceeds the strength of classical Zermelo set theory, and thus the addition of the power set axiom to CZF brings us to a fully impredicative theory.
The set-theoretic model can be criticized on the grounds that it models the type of functions as the set of all set-theoretic functions, in spite of the fact that a function in type theory is always computable, whereas a set-theoretic function may not be.
The information about an element x of a set S conditional to the set is equal to the probability that we select this element x under uniform distribution, which is a measure of our ignorance if we know the set but not which element of the set is to be selected.
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Brouwer, Luitzen Egbertus Jan | category theory | choice, axiom of | logic, history of: intuitionistic logic | logic: intuitionistic | mathematics, philosophy of | mathematics, philosophy of: intuitionism | mathematics: constructive | paradoxes: and contemporary logic | proof theory | semantics: proof-theoretic | set theory | set theory: alternative axiomatic theories | set theory: early development | set theory: non-wellfounded | type theory | type theory: intuitionistic
Curry’s paradox | epistemic paradoxes | Fitch’s paradox of knowability | Frege, Gottlob | Frege, Gottlob: theorem and foundations for arithmetic | liar paradox | logic: linear | logic: paraconsistent | logic: substructural | Quine, Willard van Orman: New Foundations | recursive functions | Russell, Bertrand | Russell’s paradox | set theory | set theory: alternative axiomatic theories | set theory: constructive and intuitionistic ZF | set theory: early development | set theory: non-wellfounded | set theory: Zermelo’s axiomatization of | Sorites paradox | Tarski, Alfred: truth definitions | truth | truth: axiomatic theories of | type theory | vagueness | Zeno of Elea | Zeno of Elea: Zeno’s paradoxes
- (usually followed by `to' or `for') on the point of or strongly disposed
- a group of things of the same kind that belong together and are so used
Example: a set of books
- put into a certain place or abstract location
- fix conclusively or authoritatively
Example: set the rules
- (mathematics) an abstract collection of numbers or symbols
Example: the set of prime numbers is infinite
- fixed and unmoving
Example: with eyes set in a fixed glassy stare
- situated in a particular spot or position
- decide upon or fix definitely
- several exercises intended to be done in series
Example: he did four sets of the incline bench press
- set down according to a plan
Example: a carefully laid table with places set for four people
- representation consisting of the scenery and other properties used to identify the location of a dramatic production
Example: the sets were meticulously authentic
- establish as the highest level or best performance
Example: set a record
- being below the horizon
Example: the moon is set
- put into a certain state; cause to be in a certain state
Example: set the house afire
- an unofficial association of people or groups
Example: the smart set goes there
- fix in a border
Example: The goldsmith set the diamond
- a relatively permanent inclination to react in a particular way
Example: the set of his mind was obvious
- determined or decided upon as by an authority
- make ready or suitable or equip in advance for a particular purpose or for some use, event, etc
- converted to solid form (as concrete)
- the act of putting something in position
Example: he gave a final set to his hat
- set to a certain position or cause to operate correctly
Example: set clocks or instruments
- a unit of play in tennis or squash
Example: they played two sets of tennis after dinner
Example: The film is set in Africa
- the process of becoming hard or solid by cooling or drying or crystallization
- the descent of a heavenly body below the horizon
Example: before the set of sun
- disappear beyond the horizon
Example: the sun sets early these days
- (psychology) being temporarily ready to respond in a particular way
Example: the subjects' set led them to solve problems the familiar way and to overlook the simpler solution
- adapt for performance in a different way
Example: set this poem to music
- put or set (seeds, seedlings, or plants) into the ground
- any electronic equipment that receives or transmits radio or tv signals
Example: the early sets ran on storage batteries
- apply or start
Example: set fire to a building
- become gelatinous
- set in type
Example: My book will be typeset nicely
- put into a position that will restore a normal state
Example: set a broken bone
- insert (a nail or screw below the surface, as into a countersink)
- give a fine, sharp edge to a knife or razor
- urge to attack someone
- equip with sails or masts
- get ready for a particular purpose or event
Example: set up an experiment
- alter or regulate so as to achieve accuracy or conform to a standard
- produce fruit
- arrange attractively
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Currys paradox | epistemic paradoxes | Fitchs paradox of knowability | Frege Gottlob | Frege Gottlob theorem and foundations for arithmetic | liar paradox | logic linear | logic paraconsistent | logic substructural | Quine Willard van Orman New Foundations | recursive functions | Russell Bertrand | Russells paradox | set theory | set theory alternative axiomatic theories | set theory constructive and intuitionistic ZF | set theory early development | set theory non-wellfounded | set theory Zermelos axiomatization of | Sorites paradox | Tarski Alfred truth definitions | truth | truth axiomatic theories of | type theory | vagueness | Zeno of Elea | Zeno of Elea Zenos paradoxes