The term "be asymptotic to" means that two things are approaching each other, but never meet. When it comes to synonyms for this concept, there are a few different options to choose from. One alternative is "approach but never reach." Another possibility is "tend toward infinity." Still another synonym could be "converge without intersecting." Ultimately, the choice of synonym will depend on context and the precise meaning intended, but these options offer some starting points for those seeking alternative ways to express the idea of approaching without touching.