All equations are identities, but not all identities are equations.

A. True
B. False

Question

All equations are identities, but not all identities are equations.

 A.	True
 B.	False

anonymous · Answer

@Jhannybean pls help

jhannybean · Answer

An identity is an equation that is dependent on it's value of x.

e.mccormick · Answer

Hmm, I would say that an identity is an equation that is true for all values of the variables.

jhannybean · Answer

example... 
$$\large \sin(x) +\cos(x) =1$$ vs $$\large \sin^2(x) +\cos^2(x) =1$$ How do you know one is identity and the other isnt?

anonymous · Answer

if it is dependant on the value of x?

jhannybean · Answer

I've got to head out, but @e.mccormick will help you out!

anonymous · Answer

ok :(

e.mccormick · Answer

That is not a bad example, but I like even easier for the base case.  To me, a good way to look at it is in the simplest case:

$x=x$ vs $x=2$

Which of these qualifies as an identity and which qualifies as an equation and note that both of them qualify as one of these things, but only one of them qualifies as the other.

The same thing could be said of Jhannybean's trig equation.

anonymous · Answer

hmm so its true because x=x but x=2 so it  is false

anonymous · Answer

im so confused >.<

e.mccormick · Answer

$x=x$ is the Reflexive Identity, all things are themselves. It is also the equation, something with an equals sign.  What about $x=2$?

hero · Answer

Hint: An equation is any statement with equal signs. An identity is only one type of equation.

hero · Answer

There are several different kinds of equations.

anonymous · Answer

oh i get it now @hero

anonymous · Answer

it would be TRUE

hero · Answer

face palm

anonymous · Answer

all equations are identities but not all identities are equations.

anonymous · Answer

:(

e.mccormick · Answer

What we were trying to point out is that all identities are equations.  They have an = in them, therefore they are equations.

anonymous · Answer

@Hero sorry that im not as smart as you.

anonymous · Answer

so false!

e.mccormick · Answer

This has nothing to do with smart.  It has to do with how much you know.  The two are not related.

hero · Answer

It's not about being smart. It's about the ability to take information, process it, digest it, understand it, and use it solve problems. It's about competency.

e.mccormick · Answer

One of the smartest people in history died saying he knew nothing.  And his intelligence has been so well regarded that he is still taught today, 2500 years or so after his death.  He was Socrates.  He was smart but knew nothing!

Just shows how little the two things are related.

There is a guy, Joshua Foer, who wrote a book about when he won the USA championship for memorizing things.  He can know a ton more than most.  He has an average IQ. 

Again, this shows that knowing and smarts are not related.

Until you learn a thing, until you understand it, until you contemplate it and make it yours, how can you talk about it fully or properly apply it?  That just means until you study things and become informed, you are uninformed.  Nothing about smarts at all!

hero · Answer

He said he knew nothing because the something he did know, in the grand scheme of things was meaningless. Knowledge by itself is meaningless. The application of knowledge, however, is what gives knowledge its usefulness. Knowledge, without application, is useless.

e.mccormick · Answer

I understand the point of Socrates.  Hehe.  I got an A in Philosophy.  My point was more to help clear up the misunderstanding StudentLearner had about smarts.  

I have met some very smart people... who were foolish.

I have met some people of average IQ that made the best of it and were very wise and good at what they did.

More about the attitude than the IQ.  A positive attitude, willingness to learn, and working hard at it can trump a smart but lazy person.

jhannybean · Answer

Intelligence does not equal knowledge, but knowledge can equal intelligence.


As for @StudentLearner's question, think of it like this: a square can be a rectangle, but a rectangle cannot be a square. You can have several equations... several values that you can input into a variable to get an outcome, such as 

3x+2y = 4

y =1

These are equations, y doesnt necessarily have to be restricted to 1, but can be a variety of numbers  that y can equal to make this statement true. 

An identity has a restriction to which makes the statement true, hence being an identity.