Axiom is a general purpose computer algebra system. It is useful for research and development of mathematical algorithms. It defines a strongly typed, mathematically correct type hierarchy. It has a programming language and a built-in compiler.
A self-evident and necessary truth, or a proposition whose truth is so evident as first sight that no reasoning or demonstration can make it plainer; a proposition which it is necessary to take for granted; as, "The whole is greater than a part;" "A thing can not, at the same time, be and not be."
An established principle in some art or science, which, though not a necessary truth, is universally received; as, the axioms of political economy.
A self evident principle or fact.
A basic assumption that is accepted without proof
1) A self evident or universally recognized truth; a maxim. 2) An established rule, principle, or law. 3) A self-evident principle or one that is accepted as true without proof as the basis for argument; a postulate.
A statement that is so obvious that it's a starting point for any research. For example, the laws of arithmetic are axioms. To say that something is axiomatic is to imply that it must be true. But beware! Sometimes axioms are revealed to be assumptions that are not always true.
a statement universally accepted as true; a maxim widely accepted on its intrinsic merit; an established rule or principle or a self-evident truth.
A statement which is accepted as a basis for further logical argument. Generally axioms are self-evident truths or principles which are basic enough that there are no principles more basic from which to prove them.
A statement that is assumed to be true.
A self-evident truth. It is the foundation of logical reasoning. Notation[ edit
a saying that widely accepted on its own merits
(logic) a proposition that is not susceptible of proof or disproof; its truth is assumed to be self-evident
a central belief or self-evident principle
a concept that is accepted without proof, perhaps because it is obvious or universally accepted (e
a dogma, and a proof is, well, a proof
a fundamentally given, directly perceived identification of a primary fact of reality
a judgement that common sense accepts without further arguments, as a matter of course
a kind of foundational assumption used in such things as mathematical and logical proof
a logical principle which is assumed to be true rather than proven, and which can be used as a premise in a deductive argument
a mathematical rule
an assumption that a logical framework is built upon
an assumption upon which a logical framework is based
an elementarybasis for a formal logic system that together with the rules of inference define alogic
an explicit or implicit fact
an irreducible primary
an irreducible proposition
an irreducible self-evident truth, implicit in all acts of cognition, which cannot be logically refuted
an "obvious" statement about natural numbers
an obvious statement, which requires no experimental check and has no exceptions
an undemonstrated proposition concerning an undefined set of elements or properties
an unproven assumption
a proposition or statement which we decide to "take for granted", without proof
a proposition that defeats its opponents by the fact that they have to accept it and use it in the process of any attempt to deny it
a proposition that is assumed to be true without providing any formal justification
a self-evident truth, a truth that does not necessitate demonstration
a simple statement (proposition) which is true for all possible circumstances
a single statement whose violation in a class file renders it unsafe
a statement not demonstrable in system a, but could be a theorem of system b
a statement of fact that is considered too simple to prove
a statement that defines a domain of validity within a context
a statement that identifies the base of knowledge and any further statement pertaining to that knowledge, a statement necessarily contained in all others, whether any particular speaker chooses to identify it or not
a statement that is accepted as true without being proved
a statement that is self-evidently true, or an agreed up 'common ground' (See the sticky in the Logic forum, which is where this thread really belongs)
a statement that is true in any universe at any time
a statement that is widely accepted as true
a statement that mathematicians accept as being true without demanding proof
a statement that seems self-evident without requiring proof
a statement universally accepted as true, like an established principal or law of science
a statement which is logically irrefutable
a statement which is taken as fundamental
a universally accepted principle or rule
a vivid statement, which requires no experimental check and has no exception
a self evident assumption.
A basic principle that cannot be deduced from other principles but is the starting point from which other statements are derived or deduced.
alg. sem.] A logical formula, built from constructors and attributes, that constrains the set of possible signs in a given sign system.
Logical condition constraining the behaviour of an object. May be expressed as an invariant, or as a precondition or postcondition on one of the object's methods.
a statement that is true by definition or so obviously true that it needn't be proved. In logic, an assumption used as an unquestioned basis for a theory.
A proposition assumed without proof for the sake of studying its consequences. See Presupposition.
An axiom is a basic precondition or assumption underlying a theory. Axioms are basic, unverifiable world view assumptions, including personal beliefs, political views, and cultural values, that form the foundation of a theory. Axioms can not be verified with real world data, and as such are largely accepted on faith. Belief in a supreme, omnipotent, omniscience being is one such axiom. The notion that people are basically good (or bad) is another. The presumption that the universe abides by cause-and-effect relationships is a key axiom for science. Back to the top
A statement that is accepted without proof.
(noun) An established rule or principle or a self-evident (obvious) truth.
is a first principle or premise. ( Study 3)
a statement that identifies the base of knowledge and of any further statement pertaining to that knowledge the identification of a primary fact of reality which cannot be analyzed (reduced to other facts or broken into component parts) and is implicit in all facts and knowledge
A mathematical statement accepted as true without being proved.
Rule without proof, nonetheless valid. Bohr, Niels Henrik David 1885-1962, established a new understanding of the atomic structure, Nobel Prize 1922.
A primary principle, which cannot and need not be proven
A basic assumption about a mathematical system from which theorems can be deduced. For example, the system could be the points and lines in the plane. Then an axiom would be that given any two distinct points in the plane, there is a unique line through them.
A self-evident proposition; a statement that needs no proof because its truth is considered obvious.
Description of self-evident truth.
An intuitively stated self-evident truth.
An axiom is any sentence, proposition, statement or rule that forms the basis of a formal system. Unlike theorems, axioms are neither derived by principles of deduction, nor are they demonstrable by formal proofs. Instead, an axiom is taken for granted as valid, and serves as a necessary starting point for deducing and inferencing logically consistent propositions.