For 18 months, Donald J. Trump the candidate described polling leads he did not always maintain and vote tallies he did not always receive — and, especially, crowd sizes he did not always have.

After his inauguration on Friday, President Trump’s first appearances also involved talking about numbers: the collective IQs of his cabinet picks, how many military members voted for him and, again, the size of a crowd, this time the one that turned out to see him sworn in.

Mr. Trump said of his inauguration crowd: “It looked, honestly, like a million and a half people. Whatever it was, it was, but it went all the way back to the Washington Monument.” In fact, the crowd was significantly smaller. A comparison of photographs from Friday to ones taken of Barack Obama’s 2009 inauguration showed that the crowd on the National Mall for Mr. Trump was about a third the size of the crowd for Mr. Obama.

But Mr. Trump, who has branded himself as everything from a world-class developer to a reality-television star to, later, a plausible presidential candidate, has long deployed what he described in his first book, “The Art of the Deal,” as “truthful hyperbole,” and others might call lies.