Difference between equations, equalities and identities.

[mzatanoskas]

I'm looking at the wikipedia page on equations.

 

But I'm getting a little confused by the different use of the terms equality, equation and identity in different situations.

 

Amongst other stuff they say:

 

[math] 2 + 3 = 5[/math]

The equations above are examples of an equality: a proposition which states that two constants are equal.

 

[math]x(x - 1) = x^2 - x [/math]

The equation above is an example of an identity...

 

...

 

Many authors reserve the term equation for an equality which is not an identity.

 

But they said that an equality was a proposition which states that two constants are equal?

 

What's the relationship between the three terms?

 

Identities are a subset of Equalities which are a subset of Equations?

 

Or

 

Identities are subset of Equations which are a subset of Equalities?

 

Or something else?

 

[the tree]

An equation is sentence with an '=' in it. An identity is equation that is true regardless of the variables involves. An equality is true only because of the constants in that particular instance.

[mzatanoskas]

Thanks tree,

 

so identities and equalities are just special types of equations right?

 

Just to check though, equalities can only feature constants? (like in the wikipedia example) or can they have a variable which has to be of a certain value ie. x + 1 = 3