Before minecraft became what it was, Minecraft was originally a pre-classic game called 'Cave Game' which lasted only for 6 days until moving to the classic version. The pre-classic version had no mobs and only contained few blocks with some of the textures taken from Notch's (Creator of Minecraft) previous game
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Notch (the creator of Minecraft), after playing Infiniminer (look it up on Wikipedia), thought it was lacking many features, so he wanted to create an Infiniminer clone of his own. And thus, Minecraft was born.
Because it descibles two of the most important things in the game, mining and crafting
Notch, the creator of Minecraft, said that he was inspired by Infiniminer, Dwarf Fortress, and Dungeon Keeper