If you use this kind of accounting the Japanese paid with about 20000 soldier
They earned it too don't you think ?
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the only difference being that when the battle concluded, all the Japanese were dead. There were no Japanese left (not many at least, the last two Japanese survivors on Iwo surrendered in 1949).
Let me put it to you like this straffo, the japanese were defeated on Iwo and the island was claimed as united states territory. We gave it back some 40 years later. We should not have. Who knows, Maybe Boeing got a big order from JAL out of the deal
Anyway, to those that know its history, that Island will always be known as Iwo Jima.