1An adverb meaning 'by all means', 'certainly', 'without fail' — used to strongly recommend something to someone or to express one's own strong wish. Usually written in kana as ぜひ for this sense.
来週の歓迎会、ぜひ参加してください。
Please be sure to come to next week's welcome party.
この本、面白いからぜひ読んでみて。
This book is interesting, so definitely give it a read.
機会があれば、ぜひ一度お目にかかりたいです。
If there's a chance, I'd very much like to meet you sometime.
「今度うちに遊びに来てね。」「うん、ぜひ。」
"Come over to my place sometime." "Yeah, I'd love to."
2The rights and wrongs of something; whether it is good or bad, for or against. Used in somewhat formal writing, as in 是非を問う ('to ask whether something is right'). Written in kanji as 是非 for this sense.
この政策の是非については、国民の間で意見が分かれている。
Opinion among the public is divided over whether this policy is right.
計画を進める前に、その是非をよく検討すべきだ。
Before going ahead with the plan, we should carefully consider its pros and cons.
原発の是非をめぐって激しい議論が続いた。
Heated debate continued over the question of nuclear power.