1. Let's start by understanding what it means for a number to be "valid" in mathematics. 2. A valid number typically means it is a well-defined number within a given context, such as real numbers, integers, rational numbers, etc. 3. For example, in the context of real numbers, any number that can be represented on the number line is valid. 4. However, some expressions may not represent valid numbers, such as division by zero or the square root of a negative number in the real number system. 5. Let's consider the expression $$\frac{5}{0}$$. This is not a valid number because division by zero is undefined. 6. Another example is $$\sqrt{-1}$$, which is not a valid real number but is valid in the complex number system as $$i$$. 7. To check validity, always consider the domain and the operations involved. 8. If you have specific examples or expressions, we can analyze their validity step-by-step.