what is the meaning of axiom?

Answer 1

a statement that requires no proof, because it is self-evident.

for instance, Euclid's classic first axiom is:
For every point P and every point Q not equal to P there exists a unique line that passes through P and Q.

(which means - every two points are connected by a straight line. you don't need to prove that - because it's obviously true.)

Answer 2

Axiom
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For other uses, see Axiom (disambiguation).
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. In many usages, "axiom," "postulate," and "assumption" are used interchangeably.

In certain epistemological theories, an axiom is a self-evident truth upon which other knowledge must rest, and from which other knowledge is built up. An axiom in this sense can be known before one knows any of these other propositions. Not all epistemologists agree that any axioms, understood in that sense, exist.

In logic and mathematics, an axiom is not necessarily a self-evident truth, but rather a formal logical expression used in a deduction to yield further results. To axiomatize a system of knowledge is to show that all of its claims can be derived from a small, well-understood set of sentences. This does not imply that they could have been known independently; and there are typically multiple ways to axiomatize a given system of knowledge (such as arithmetic). Mathematics distinguishes two types of axioms: logical axioms and non-logical axioms.

Answer 3

I believe all solutions so some distance. In maths, as in something else, you want to understand the position to start up from as a way to make experience of the position you flow from there. In maths, you start up with the Peano postulates, or axioms, which outline (or create in case you want) the organic numbers. added axioms outline the needed operations which will properly be utilized to numbers, and inform you the way they artwork (a+b=b+a is an party). each little thing else contained in the arithmetic of numbers persist with from those.

Answer 4

An axiom is a sentence in first order logic that is assumed to be true without proof. In practice, we use axioms to refer to the sentences that cannot be represented using only slots and values on a frame.
Axioms must be entered in prefix notation. Use => to indicate logical implication, <=> to indicate logical equivalence, and to indicate conjunction, or to indicate disjunction, not to indicate negation, and exists to indicate existential quantification. Free variables are assumed to be universally quantified. Variable names must start with a question mark.

Answer 5

ax·i·om (ăk'sē-əm)
n.
A self-evident or universally recognized truth; a maxim: “It is an economic axiom as old as the hills that goods and services can be paid for only with goods and services” (Albert Jay Nock).
An established rule, principle, or law.
A self-evident principle or one that is accepted as true without proof as the basis for argument; a postulate.
[Middle English, from Old French axiome, from Latin axiōma, axiōmat-, from Greek, from axios, worthy.]







axiom

noun

A broad and basic rule or truth: fundamental, law, principle, theorem, universal.



axiom
n
Definition: principle
Antonyms: absurdity, ambiguity, foolishness, nonsense, paradox


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axiom

In mathematics or logic, an unprovable rule or first principle accepted as true because it is self-evident or particularly useful (e.g., "Nothing can both be and not be at the same time and in the same respect"). The term is often used interchangeably with postulate, though the latter term is sometimes reserved for mathematical applications (such as the postulates of Euclidean geometry). It should be contrasted with a theorem, which requires a rigorous proof.






axiom, in mathematics and logic, general statement accepted without proof as the basis for logically deducing other statements (theorems). Examples of axioms used widely in mathematics are those related to equality (e.g., “Two things equal to the same thing are equal to each other”; “If equals are added to equals, the sums are equal”) and those related to operations (e.g., the associative law and the commutative law). A postulate, like an axiom, is a statement that is accepted without proof; however, it deals with specific subject matter (e.g., properties of geometrical figures) and thus is not so general as an axiom. It is sometimes said that an axiom or postulate is a “self-evident” statement, but the truth of the statement need not be evident and may in some cases even seem to contradict common sense. Moreover, a statement may be an axiom or postulate in one deductive system and may instead be derived from other statements in another system. A set of axioms on which a system is based is often wished to be independent; i.e., no one of its members can be deduced from any combination of the others. (Historically, the development of non-Euclidean geometry grew out of attempts to prove or disprove the independence of the parallel postulate of Euclid.) The axioms should also be consistent; i.e., it should not be possible to deduce contradictory statements from them. Completeness is another property sometimes mentioned in connection with a set of axioms; if the set is complete, then any true statement within the system described by the axioms may be deduced from them.








axiom (ak-see-uhm)

In mathematics, a statement that is unproved but accepted as a basis for other statements, usually because it seems so obvious.


The term axiomatic is used generally to refer to a statement so obvious that it needs no proof.












axiom

IN BRIEF: An accepted principle.

It has long been an axiom of mine that the little things are infinitely the most important. — Sir Arthur Conan Doyle (1859-1930)
Tutor's tip: Grandparents usually tell children "axioms" (self-evident truths) about life. Physicists talk about "axions" (hypothetical particles of matter) when trying to explain the universe.







The noun axiom has 2 meanings:

Meaning #1: a saying that widely accepted on its own merits
Synonym: maxim


Meaning #2: (logic) a proposition that is not susceptible of proof or disproof; its truth is assumed to be self-evident













axiom
This article does not cite its references or sources.
You can help Wikipedia by introducing appropriate citations. This article has been tagged since November 2006.
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. In many usages, "axiom," "postulate," and "assumption" are used interchangeably.

In certain epistemological theories, an axiom is a self-evident truth upon which other knowledge must rest, and from which other knowledge is built up. An axiom in this sense can be known before one knows any of these other propositions. Not all epistemologists agree that any axioms, understood in that sense, exist.

In logic and mathematics, an axiom is not necessarily a self-evident truth, but rather a formal logical expression used in a deduction to yield further results. To axiomatize a system of knowledge is to show that all of its claims can be derived from a small set of sentences that are independent of one another. This does not imply that they could have been known independently; and there are typically multiple ways to axiomatize a given system of knowledge (such as arithmetic). Mathematics distinguishes two types of axioms: logical axioms and non-logical axioms.

Answer 6

If something is AXIOMATIC, it means that it is generally understood
"It is axiomatic in politics that the incumbent representative will be re-elected if he is popular with the people in his district."

Therefore, and axiom is a thing (noun) that is understood.

Good luck from a high school english teacher!

Answer 7

A statement that can be taken as a given. It is something that may or may not be proven true, but is always treated as if it is true.

Answer 8

A statement that can't be proved so needs to be accepted

Answer 9

a self evident truth which no need any proves,a univerversally accepted principle and rule

Answer 10

a true statement which is accepted by all likes scientific law etc.