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Identity Element শব্দের বাংলা অর্থ: পরিচয় উপাদান
Identity Element Meaning In Bengali পরিচয় উপাদান
Identity Element
Definition
1) An element in a set that leaves other elements unchanged when combined with them using a specified binary operation.
2) A neutral element in a set with a binary operation that behaves as an identity under the operation.
3) A specific element in a mathematical structure such as a group that combines with other elements to leave them unchanged when operated on.
Examples
Identity Element Example in a sentence
1) In the set of real numbers, the identity element for addition is 0.
2) The matrix with all diagonal elements equal to 1 is the identity element for matrix multiplication.
3) For multiplication, the identity element in the set of integers is 1.
4) The identity element for the operation of rotation in geometry is the identity transformation.
5) In modular arithmetic, the identity element for addition modulo 7 is 0.
6) The identity element in the set of rational numbers under multiplication is 1.
7) The identity element for exponentiation is 1, as any number raised to the power of 1 remains unchanged.
8) In group theory, the identity element is denoted as 'e' and satisfies the property that when combined with any element in the group, the result is that element.
9) The identity element for the operation of reflection in geometry is the line of reflection itself.
10) For complex numbers, the identity element under multiplication is the complex number 1.
Part of Speech
Identity Element (Noun)
Synonyms
Encyclopedia
An element in a set that leaves other elements unchanged when combined with them using a specified binary operation.
A neutral element in a set with a binary operation that behaves as an identity under the operation.
A specific element in a mathematical structure such as a group that combines with other elements to leave them unchanged when operated on.