Equation and identity

[shahar]

What is the differences between those two?
Identity - זהות
Equation - משוואה
And: What is the differences between identity to theorem?
Identity - זהות
Theorem - משפט
Why does Pitagoras theorem not be known as Pitagoras indetity?
I aware of grammar errors but it is hard to me to write it correctly. So please help me to edit the post.

 

[blamocur]

Equations is an expression with an unknown whose value can usually be found from the equation. E.g., $5x+3 = 8$, where we can figure out that $x=1$.

Identity is something which is always true. It might or might not contain unknowns. E.g.: $(x+3)^2 = x^2 + 6x + 9$, or: $e^{i\pi}+1 = 0$.

Theorems are statements which have a proof. Statements without a proof are usually called hypotheses. Theorems often, but not always, can be about identities.

 

[Dr.Peterson]

What is the difference between these two?
Identity - זהות
Equation - משוואה

An equation is a statement that two expressions are equal (for some particular values of any variables they contain). It says that two things happen to have the same value.

An identity is an equation that is true for any values of its variables (again, if any). It says that they are the very same thing. They are identical.

And: What is the difference between identity and theorem?
Identity - זהות
Theorem - משפט

A theorem is a statement that some fact is true; that fact may be an identity, or it may be an equation that is true under some stated conditions, or it may not involve an equation at all.

Why is Pitagoras theorem not known as Pitagoras identity?

It is an equation that is true, not for any values of the variables, but when those variables are the sides of a right triangle.

 

[ashley2]

What is the differences between those two?
Identity - זהות
Equation - משוואה
And: What is the differences between identity to theorem?
Identity - זהות
Theorem - משפט
Why does Pitagoras theorem not be known as Pitagoras indetity?
I aware of grammar errors but it is hard to me to write it correctly. So please help me to edit the post.

• An equation is a mathematical statement that says two things are equal. It can be true sometimes (like 2x = 4 is only true when x = 2).
• An identity is an equation that is always true for all values of the variable (like sin²x + cos²x = 1).
• A theorem is a proven mathematical statement. It might describe relationships that are only true under certain conditions, and it needs proof.

So, the Pythagorean theorem (a² + b² = c²) is a specific result about right-angled triangles, not something that is always true for all a, b, and c. That’s why it’s called a theorem, not an identity.