| Line 344: |
Line 344: |
| | | | | | |
| | <math>\begin{array}{l} | | <math>\begin{array}{l} |
| − | Q ~\operatorname{is}~ P^{\prime}, P^{\prime\prime}, P^{\prime\prime\prime}; | + | Q ~\text{is}~ P^{\prime}, P^{\prime\prime}, P^{\prime\prime\prime}; |
| | \\[4pt] | | \\[4pt] |
| − | S^{\prime}, S^{\prime\prime}, S^{\prime\prime\prime}, ~\operatorname{are}~ R\operatorname{'s}; | + | S^{\prime}, S^{\prime\prime}, S^{\prime\prime\prime}, ~\text{are}~ R\operatorname{'s}; |
| | \\[4pt] | | \\[4pt] |
| − | \operatorname{Hence,}~ Q ~\operatorname{is~an}~ R. | + | \text{Hence,}~ Q ~\text{is an}~ R. |
| | \end{array}</math> | | \end{array}</math> |
| | |- | | |- |
| Line 360: |
Line 360: |
| | S^{\prime}, S^{\prime\prime}, S^{\prime\prime\prime}, ~\text{etc., are samples of the}~ X\operatorname{'s}, | | S^{\prime}, S^{\prime\prime}, S^{\prime\prime\prime}, ~\text{etc., are samples of the}~ X\operatorname{'s}, |
| | \\[4pt] | | \\[4pt] |
| − | c
| + | Q ~\text{is found to be}~ P^{\prime}, P^{\prime\prime}, P^{\prime\prime\prime}, ~\text{etc.}; |
| | & | | & |
| − | d
| + | S^{\prime}, S^{\prime\prime}, S^{\prime\prime\prime}, ~\text{etc., are found to be}~ R\operatorname{'s}; |
| | \\[4pt] | | \\[4pt] |
| − | e
| + | \text{Hence, hypothetically,}~ Q ~\text{is an}~ X. |
| | & | | & |
| − | f
| + | \text{Hence, inductively, every}~ X ~\text{is an}~ R. |
| | \end{array}</math> | | \end{array}</math> |
| | |} | | |} |