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The Fundamental Rights in India enshrined in part III (Article 12–35) of the Constitution of India guarantee civil liberties such that all Indians can lead their lives in peace and harmony as citizens of India. [1] These rights are known as "fundamental" as they are the most essential for all-round development i.e., material, intellectual ...
[1] Mathematics is essential in the natural sciences, engineering, medicine, finance, computer science, and the social sciences. Although mathematics is extensively used for modeling phenomena, the fundamental truths of mathematics are independent of any scientific experimentation.
In mathematics, equality is a relationship between two quantities or expressions, stating that they have the same value, or represent the same mathematical object. [1] [2] Equality between A and B is written A = B, and pronounced "A equals B". In this equality, A and B are distinguished by calling them left-hand side (LHS), and right-hand side ...
In mathematics, Jensen's inequality, named after the Danish mathematician Johan Jensen, relates the value of a convex function of an integral to the integral of the convex function. It was proved by Jensen in 1906, [1] building on an earlier proof of the same inequality for doubly-differentiable functions by Otto Hölder in 1889. [2]
The Constitution (First Amendment) Act, 1951, enacted in 1951, made several changes to the Fundamental Rights provisions of the Indian constitution.It provided means to restrict freedom of speech and expression, validation of zamindari abolition laws, and clarified that the right to equality does not bar the enactment of laws which provide "special consideration" for weaker sections of society.
The Fundamental Rights and Directive Principles had their origins in the Indian independence movement, which strove to achieve the limits of liberty and social welfare as the goals of an independent Indian state. [1] The development of constitutional rights in India was inspired by historical documents such as England's Bill of Rights, the ...
where , is the inner product.Examples of inner products include the real and complex dot product; see the examples in inner product.Every inner product gives rise to a Euclidean norm, called the canonical or induced norm, where the norm of a vector is denoted and defined by ‖ ‖:= , , where , is always a non-negative real number (even if the inner product is complex-valued).
In mathematics, a binary relation on a set is reflexive if it relates every element of to itself. [1] [2] An example of a reflexive relation is the relation "is equal to" on the set of real numbers, since every real number is equal to itself.