For words like equation, expression, and term, do we have more formal definitions at
- any level (perhaps from set theory, logic, or algebra); or
- at a level suitable for secondary/high-school students?
Or are these simply words that are used loosely and informally?
At the secondary/high-school level, we might usually simply say something like
an equation has an equals sign, an expression doesn't.
Or we might give an example like the picture below. But I was wondering if we could do a little better.
A term is generally compromised of a coefficient,a variable and an exponent.
For example, $-4x^3$ is a term with coefficient $-4$, variable $x$ and exponent $3$
An expression is generally compromised of more than one term.
For example $$3x^2-4y+2$$ is an expression consisting of three terms.
An equation is the statement of equality between two expressions.
The statement may be true for some values of variables called the solutions to equation.
For example $$ x^2-3x+2=0 $$ is an equation which is true if $x=2$ or $x=1$
An identity is the statement of equality between two expressions whose values are the same for all values of the variables.
For example $(x+y)^2= x^2+2xy+y^2.$