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The leptonic di-flavor violation (LFV) processes $\mu^\pm \mu^\pm \rightarrowe^\pm e^\pm $, $\mu^\pm \mu^\pm \rightarrow \tau^\pm \tau^\pm $ and theleptonic di-number violation (LNV) processes $\mu^\pm \mu^\pm \rightarrow W^\pm_iW^\pm _j$ ($i,\;j=1,\;2$) at the same-sign high energy $\mu^\pm \mu^\pm $colliders are studied. The new physics (NP) factors that may play roles inthese processes are highlighted by cataloging them into three types. Takinginto account the experimental constraints, the processes at $\mu^\pm\mu^\pm$colliders are computed and the results are presented properly. The results leadto the conclusion that observing the NP factors through the LFV and LNVprocesses at TeV-energy $\mu^\pm\mu^\pm$ colliders has significant advantagesthat cannot be achieved elsewhere. Therefore, in developing the techniques ofmuon acceleration and collisions, the option of building the same-sign muonhigh-energy colliders should be considered seriously too.

The leptonic di-flavor and di-number violation processes at high energy $\mu^\pm\mu^\pm $ colliders