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There are several ways to create some kind of infinite plane. The best way would depend on what exactly you are after.
1. Make sure nothing is selected.
2. Click the world button and then click on texture button. This should make the texture applicable to the world instead of to some object.
3. Add some texture. Under the influence tab check "horizon".
A horizon line would appear when the scene is on the surface of a planet (Earth?) and there is infinite ground all around with a sky above the horizon line.