Ternary scale theorems: Difference between revisions
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* |'''u'''<sub>1</sub>|<sub>'''Y'''</sub> = |'''u'''<sub>2</sub>|<sub>'''Y'''</sub> + 1 | * |'''u'''<sub>1</sub>|<sub>'''Y'''</sub> = |'''u'''<sub>2</sub>|<sub>'''Y'''</sub> + 1 | ||
* |'''u'''<sub>1</sub>|<sub>'''Z'''</sub> = |'''u'''<sub>2</sub>|<sub>'''Z'''</sub> − 1 | * |'''u'''<sub>1</sub>|<sub>'''Z'''</sub> = |'''u'''<sub>2</sub>|<sub>'''Z'''</sub> − 1 | ||
* |'''v'''|<sub>'''Y'''</sub> = |'''v'''|<sub>'''Z'''</sub> = |'''u'''<sub>1</sub>|<sub>'''Y'''</sub>. | * |'''v'''|<sub>'''Y'''</sub> = |'''v'''|<sub>'''Z'''</sub> = |'''u'''<sub>1</sub>|<sub>'''Y'''</sub> = min(|'''u'''<sub>1</sub>|<sub>'''Y'''</sub>, |'''u'''<sub>2</sub>|<sub>'''Y'''</sub>). | ||
This proves that the set of ''j''-steps is balanced. The argument for when ''m'' is even is similar. {{qed}} | This proves that the set of ''j''-steps is balanced. The argument for when ''m'' is even is similar. {{qed}} | ||