Difference between an Equation and an Identity?

[preekap]

Can u guys tell me the difference b/w an Equation and an Identity?

Thx

 

[CompuChip]

I use the terms quite sloppily myself, but it appears that an identity expresses an equality regardless of the values of any variables. So for example,
$$x(x - 1) = x^2 - x$$
is an identity, because it is true for any values of x that you plug in. However,
$$x(x - 1) = 0$$
is an equation, which only holds when specific values for x are plugged in (called the solutions to the equation).

 

[matt grime]

A more interesting identity than one which is just multiplying out a bracket would be something like

$$\sin^2 x + \cos^2 x \equiv 1$$

Note the three lined symbol which one is supposed to use for identities, rather than the = symbol. Of course, this is something that most of us (me included) would use only if it was really necessary to clarify such a point.

 

[kts123]

^ That's odd, I've covered lots of identities and I've never once seen that in any textbook (nor during the bajillion trig identities I was forced to prove in high school.)

 

[matt grime]

Surely it's the first one you prove/meet, and is merely Pythagoras's theorem.

 

[HallsofIvy]

^ That's odd, I've covered lots of identities and I've never once seen that in any textbook (nor during the bajillion trig identities I was forced to prove in high school.)

It's not clear whether you are talking about CompuChip's x(x-1)= x²- x or matt grimes' sin²x+ cos²x= 1 but you will find the first in any elementary algebra text and the second in any trigonometry text.

 

[maze]

wooosh

 

[Integral]

I thought he was talking about the 3 line identical equal to symbol.