An equation is any statement with an equals sign in it.

Equations come in a variety of flavours. A simple (and simplistic) classification of equations could include:

Equations

Mathematical statement which is true for a limited number of values of its variable.

  • $3x+2=-7$ is true for one value of the variable x
  • $sin(x)=0.5$ is true for an infinite number but not all of values of x

Identities

Statements which are true for all values of the variable.

  • $3(x+2)=3x+6$
  • $2^n=\sum_{i=0}^{i=n}{n\choose~i}$

Propositions

Statements which are either true or false

  • 2 + 3 = 5
  • 1 + 1 = 3

However, this classification does not include differential equations, integral equations, functions, etc.

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