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Related to much less: Much less than
1. A lot less. We've had much less foot traffic since construction started. This magazine has much less content than it used to.
2. And especially not; and even less so. The phrase is used to indicate that something is especially not the case, even less so than what was previously mentioned. We don't have enough money for new car, much less a luxury SUV. He barely looked at me, much less smiled.
And certainly not, as in He rarely talks about his outside activities, much less his family. The earliest record of this idiom is in John Milton's Paradise Lost (1671): "The world thou hast not seen, much less her glory."