In the following examples, 'N' represents any numeral, 'L' represents the logarithm operator:

- N÷0 is undefined
- 0^0 is undefined (it does not equal zero; it does not equal one)
- 0√1 is undefined
- 0√0 is undefined
- 0LN is undefined
- 0L0 is undefined
- NL0 is undefined
- 1L1 is undefined
- Only positive roots are allowed. So, for example, 2√4 has two roots: 2 and -2. Only the positive root (also known as the 'principle root') is used in Goals and Solutions. If you wanted '-2' in your Goal or Solution, you would have to subtract it from zero, for example: 0-2√4 = -2