这是一句不完整的话,the minute其实是 时间状语从句的引导词,翻译成：“一.就.”
或者翻译成：某人做...的那一刻.
the minute you think of giving up 翻译成,你一想到放弃,或者你想到放弃的那一刻,
eg.The minute he told me the news,I fainted.他一告诉我消息,我就晕了.
类似结构 The second ,the moment可以等同the minute
eg.The second he arrived home ,he turned the TV.他一回家就打开了电视
希望回答能解答你的疑惑,不懂追问.