what does the symbol "≡" means? and how to read this equation a ≡ b?

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- May 7th 2011, 12:38 AMKalodaa ≡ b ?
what does the symbol "≡" means? and how to read this equation a ≡ b?

- May 7th 2011, 01:06 AMHappyJoe
It really depends on the context.

If you are working modulo some number n, then $\displaystyle a\equiv b$ means that a and b are congruent modulo n, which in turn means that n divides the difference a-b. For instance, $\displaystyle 7\equiv 3\pmod{2}$, since 2 divides the difference 7-3.

If a and b are functions from the same domain, it could also mean that the two functions are identical, i.e. for all values of x in the domain, we have that a(x)=b(x). For example, the two functions $\displaystyle a(x)=\cos^2(x)+\sin^2(x)$ and $\displaystyle b(x)=1$ are identical on the set of real numbers.

It might not be one of these two options, though. Some context will help in answering the question.