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"I now determined upon a regular siege to 'out-camp the enemy,' as it were, and to incur no more losses. The experience of the 22d convinced officers and men that this was best, and they went to work on the defenses and approaches with a will. With the navy holding the river the investment of Vicksburg was complete. As long as we could hold our position, the enemy was limited in supplies of food, men, and munitions of war, to what they had on hand. These could not last always."
I would call that attrition.
This is the statement I object to: “Grant had no strategy beyond using the north's advantages in manpower and equipment to wear down his opponents in a war of attrition.”