This is a word that people don't usually stop and define. They use it to link two seemingly contradictory thoughts. Nonetheless, it does have a definition. It means "in spite of."

Break this word up to examine its meaning: None-the-less means that the statement you've just made does not diminish or make less what comes next. We are not at all prepared to climb this mountain, nonetheless we are going to try.

Definitions of nonetheless

adv despite anything to the contrary (usually following a concession)

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