for all
Prepositional phrase
  1. In spite of, despite.
    For all his protests, he was forced to have a bath.
    • 1988, Michael Hopkinson, [https://books.google.co.in/books?id=BO34AwAAQBAJ&pg=PT382&dq=Collins'+death+can+be+put+down+to+his+devil-may-care+attitude-+his+decision+to+journey+through+hostile+territory+in+a+large+convoy,+the+inadequate+choice+of+the+members+of+the+convoy,+and+the+tactics+he+adopted+in+the+ambush.&hl=en&sa=X&ved=0ahUKEwjYg4ui76rjAhUIVH0KHfgYATcQ6AEIJzAA#v=onepage&q=Collins'%20death%20can%20be%20put%20down%20to%20his%20devil-may-care%20attitude-%20his%20decision%20to%20journey%20through%20hostile%20territory%20in%20a%20large%20convoy%2C%20the%20inadequate%20choice%20of%20the%20members%20of%20the%20convoy%2C%20and%20the%20tactics%20he%20adopted%20in%20the%20ambush.&f=false Green Against Green: The Irish Civil War]:
      Michael Collins (Irish leader)' death can be put down to his devil-may-care attitude—his decision to journey through hostile territory in a large convoy, the inadequate choice of the members of the convoy, and the tactics he adopted in the ambush. For all the debate about ballistics and entry and exit wounds, and the use of powerful historical imaginations, it matters more that Collins was killed than how he was killed. Concentration on the events at Béal na mBláth has, moreover, often meant a failure to place them in the overall context of the war.
  2. (mathematics, literally) Applying to every element of a set.
    For all x in A, x^2 is even.



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