Final answer:
Some expressions in mathematics can be simplified while others are undefined. Division by zero, square roots of negative numbers, and logarithms of zero are examples of expressions that are undefined.
Step-by-step explanation:
In mathematics, some expressions can be simplified while others cannot. When an expression is undefined, it means that it does not have a valid numerical value. Here are some examples:
- The expression 1 ÷ 0 is undefined because you cannot divide any number by zero.
- The expression √(-1) is undefined because square roots of negative numbers are not defined in the real number system.
- The expression log(0) is undefined because the logarithm of zero is not defined.
When simplifying expressions, be mindful of any restrictions or conditions that may make the expression undefined.