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Is the continuum hypothesis true?
Continuum hypothesis was proven, with an proving method called "forcing", to be undecidable under commonly accepted axioms of the set theory. This means that neither continuum hypothesis nor it's negation follows from this axioms just like one axiom (or it's negation) in some consistent axiomatic system does not follow from other axioms. Therefore, continuum hypothesis or it's negation could be added as an additional axiom to existing commonly accepted axioms of the set theory.
What are the types of axioms?
There are two types of mathematical axioms: logical and non-logical. Logical axioms are the "self-evident," unprovable, mathematical statements which are held to be universally true across all disciplines of math. The axiomatic system known as ZFC has great examples of logical axioms. I added a related link about ZFC if you'd like to learn more. Non-logical axioms, on the other hand, are the axioms that are specific to a particular branch of mathematics, like arithmetic, propositional calculus, and group theory. I added links to those as well.
Which is a dimension or assumption of the marginal-utility theory of consumer behavior?
The consumer has a small income.
What is ordinal approach to the theory of consumer behavior?
ordinal approach to the theory of consumer behaviour is consumer's ability to rank his preference for various combination of products. It uses Indifference curve to analyse these preferences.
Consumer equlibrium with the help of law of dimnishing marginal utility?
types of equilibrium in consumer theory
What is Godel's theorem and the limits of science?
Gödel's theorem states that it is impossible to make a complete set of mathematical axioms that can explain every truth about arithmetics. This means that no matter how you define the fundamental axioms of mathematics, there have to be certain statements that are true within mathematics that can not be formally proved by using the fundamental axioms. This theorem pretty much shattered the mathematician's dream of describing all of mathematics within a framework of a limited number of logical axioms. Nevertheless, the axiomatic Zermelo-Frankel set theory is able to explain all of the known mathematics from fundamental axioms, but philosophically it is still not a complete theory. Although the theorem is extremely complicated, it can be understood by anybody with a basic mathematical knowledge. This link shows a version of the proof: http://www4.ncsu.edu/unity/lockers/users/f/felder/public/kenny/papers/godel.html
What is accepted without proof in a logical system?
Axioms and Posulates -apex
What is the role theory and how does it help us to understand consumer behavior?
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Is the product of rational numbers equal a rational number?
The short answer to your question: yes. This is one of the central axioms of math. If you'd like a bit more detail, try researching number theory.
What is the Tamil meaning for theory?
theory means writing paper.
What is plenary theory?
Plenary theory is a legal concept that refers to an unrestricted or complete power or authority held by a particular governing body or individual. It implies that the entity in consideration has the full and absolute authority to act or make decisions within its designated jurisdiction. Plenary theory is often associated with governmental bodies and regulatory agencies.
What is the difference between theory and theorem?
A theorem is a step in a mathematical theory that allows, starting from hypotheses, to demonstrate rigorously some conclusion. A theory is composed by five elements in general - axioms; - primary entities; - logical rules; - derived entities; - theorems. axioms and primary entities are the base of the theory: they are objects that are not defined from within the theory and relationships among these objects that are simply assumed three. In standard geometry the point, the straight line, the plane are primary objects while the assumption that the straight line that passes y two given points always exists and it is unique is an axiom. Every theory starts from axioms and primary objects. Logical rules are the rules that are assumed to guarantee that, if premises are true, the consequences derived using such rules are also true. Standard logical rules are generally assumed like A=B => B=A and the so. In mathematics standard mathematical demonstration rules like the modus ponens are also adopted. In selected theories, probability rules are also used as logical rules. Derived objects are objects defined inside the theory, like the triangle or the polygon in standard geometry. We have just see what a theorem is: it is the instrument allowing to derive new properties from objects axioms and already derived properties. If we deal with a scientific theory, like a physical theory, a mathematical structure is not enough to use the theory to interpret nature. We must have the so called interpretation scheme allowing us to translate experimental results into relationships between the objects of the theory and back. For example we must connect the theory object we call electron, with its properties like the motion equation, the charge and so on, with experimental observations like interference figures in electrons beam experiments that we interpret at the theory light as the sign of electrons presence.
