Question

identity , equal , equivalent --- are used in mathematics . are identity and equal both same ?? if same then we can put = sign in every identity . but Identities are sometimes indicated by the triple bar symbol ≡ instead of = ------ what does it mean?? if we use the triple bar ≡ , then it becomes equivalent .now we can say identities are sometimes equivalent. is it true? it becomes confusing .please explain with example . please help to learn the actual concept.

Answer 1

Answer on Question #51694 – Math – Discrete Mathematics

identity, equal, equivalent --- are used in mathematics. are identity and equal both same ?? if same then we can put = sign in every identity. but Identities are sometimes indicated by the triple bar symbol ≡ instead of = --- what does it mean?? if we use the triple bar ≡, then it becomes equivalent. now we can say identities are sometimes equivalent. is it true? it becomes confusing. please explain with example. please help to learn the actual concept.

Solution

When A and B are functions of some variables, then identity $A \equiv B$ means that A and B define the same function i.e. $A = B$ for any values of variables.

For example, $\sin 2x = 2 \sin x \cos x$ or $(x + y)^2 = x^2 + 2xy + y^2$ are true for any values of variables.

Identities are denoted by the triple bar sign ≡, sometimes by the equality sign =.

Equality expresses a relationship between given quantities asserting that the quantities have the same value.

For example, $x^{2} = 4x$ which is true only when $x = 0$ or $x = 4$.

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