What is the solution set for an equation in which all numbers work?

How big is the solution set for an equation that cannot be solved?

In mathematics, the solution set of an equation refers to the set of all values or numbers that satisfy the equation.

If an equation is such that all numbers can be substituted into it and make it true, then the solution set is said to be all real numbers. This means that the equation holds true for any value of x. For example, the equation 5x - 7 = 0 has a solution set of all real numbers, because any value of x will make the equation true.

On the other hand, if an equation cannot be solved, it means that there are no numbers or values of x that satisfy the equation. In this case, the solution set is said to be empty or null, denoted by ∅ or {} (an empty set). An example of such an equation is x + 1 = x + 2, which has no solutions.