Asymptotically is a word used to describe something that approaches a limit or a particular point without ever reaching it. Some synonyms for this word include gradually, infinitesimally, slowly, or progressively. Similarly, asymptotically can also be replaced by the words approximately, closely, or nearly to suggest a limited but close approach to a given value. In mathematical terms, the term 'asymptotically equivalent' could be replaced with the term 'as good as or close to', while 'asymptotic behavior' could be replaced by words such as 'approach pattern' or 'tendency towards.' Therefore, these synonyms for 'asymptotically' can be used to enhance the writing's diversity and clarity when conveying complex mathematical concepts.