Identically equal to?

[m@tty]

When do we need to use the "identically equal to" sign in favour of a normal equal sign? Does it only apply when creating partial fractions? And is it even necessary to use then?

Thanks

[m@tty]

I don't know, maybe it is equivalent. It is used when creating partial fractions in the MathsQuest Specialist book.
Eg.


Then do the same to find A, hence splitting the fraction. That's the only place I've seen it used.

[Martoman]

What this means is equal to IN EVERY CASE.

Because you can reduce P(x) to:
P(x) = A(x-b) + B(x-a) plugging in the points "b" and "a" into this equation and getting a solution is valid. Whereas if you plugged this into the original equation, then this would cause the universe to explode - that is, divide by zero.

[QuantumJG]

When do we need to use the "identically equal to" sign in favour of a normal equal sign? Does it only apply when creating partial fractions? And is it even necessary to use then?

Thanks

Doesn't '' mean equivalent to?

According to wikapedia '' is the same as '~', is this true?

[the.watchman]

This symbol can also be used for congruence (both geometric and mathematical congruence).

[TrueTears]

Use it in modular arithmetic.