Trump felt he served in the military, however he did not

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I wonder whose military Trump feels he served in? Politico shares excerpts from an upcoming book wherein Donald mistakes being sent to military academy as service to his nation.

From Politico:

Trump, who received multiple draft deferments and a high draft lottery number during the Vietnam War, took off a shoe to explain the heel spurs that prompted the medical deferments. The Vietnam war, he added, "was a mistake."

"My number was so incredible and it was a very high draft number. Anyway so I never had to do that, but I felt that I was in the military in the true sense because I dealt with those people," Trump told the author in another excerpt.